Gr 11 Math Ch 6 SUM: Trigonometry

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Questions and Answers

What is the purpose of trigonometric identities?

  • To solve equations that contain only sine ratios
  • To prove other equations
  • To simplify a given expression so that it contains sine and cosine ratios only (correct)
  • To find the value of tangent in terms of sine and cosine

What is the quotient identity for tangent in terms of sine and cosine?

  • tan θ = sin θ / cos θ (correct)
  • tan θ = sin² θ / cos² θ
  • tan θ = sin θ × cos θ
  • tan θ = cos θ / sin θ

Why is tan θ undefined when θ = k × 90°, where k is an odd integer?

  • Because tan θ = 0
  • Because cos θ = 0 (correct)
  • Because sin θ = 0
  • Because θ is undefined

What is the square identity, also known as the Pythagorean identity?

<p>sin² θ + cos² θ = 1 (D)</p> Signup and view all the answers

What is the first step in proving an identity?

<p>Change all trigonometric ratios to sine and cosine (D)</p> Signup and view all the answers

What is another form of the square identity?

<p>sin² θ = 1 - cos² θ (C)</p> Signup and view all the answers

Why is it usually better to choose the more complicated side of the equation to simplify?

<p>Because it is usually closer to the desired form (C)</p> Signup and view all the answers

What is the benefit of using trigonometric identities?

<p>They enable us to simplify a given expression so that it contains sine and cosine ratios only (C)</p> Signup and view all the answers

What is the purpose of replacing 1 with sin^2 θ + cos^2 θ when simplifying trigonometric expressions?

<p>To make simplifying easier (C)</p> Signup and view all the answers

Which trigonometric identity is defined for all values of θ, except where cos θ = 0?

<p>tan θ = sin θ / cos θ (C)</p> Signup and view all the answers

What is the alternative form of the square identity sin^2 θ + cos^2 θ = 1?

<p>sin^2 θ = 1 - cos^2 θ (B)</p> Signup and view all the answers

What is the reduction formula for sin(180° - θ)?

<p>sin θ (C)</p> Signup and view all the answers

What is the purpose of using the square root sign in trigonometric expressions?

<p>To indicate that we need to use the square identity (D)</p> Signup and view all the answers

What is the reduction formula for cos(180° - θ)?

<p>-cos θ (A)</p> Signup and view all the answers

What is the condition for the quotient identity tan θ = sin θ / cos θ to be defined?

<p>cos θ ≠ 0 (A)</p> Signup and view all the answers

Which of the following is a trigonometric identity?

<p>tan θ = sin θ / cos θ (D)</p> Signup and view all the answers

If point P has coordinates (√3, 1), what are the coordinates of P' if P and P' are symmetrical about the origin?

<p>(-√3, -1) (D)</p> Signup and view all the answers

What is the value of sin(180° + θ)?

<p>-sin θ (D)</p> Signup and view all the answers

If points P and P' are symmetrical about the x-axis, what are the coordinates of P'?

<p>(x, -y) (C)</p> Signup and view all the answers

What is the value of cos(-θ)?

<p>cos θ (B)</p> Signup and view all the answers

What is the value of tan(360° - θ)?

<p>-tan θ (C)</p> Signup and view all the answers

What is the value of sin(90° - θ)?

<p>cos θ (A)</p> Signup and view all the answers

What is the value of cos(90° + θ)?

<p>-sin θ (B)</p> Signup and view all the answers

What is the relationship between sin(90° - θ) and cos θ?

<p>sin(90° - θ) = cos θ (B)</p> Signup and view all the answers

How can sin 54° be expressed as a trigonometric ratio of 36°?

<p>cos 36° (D)</p> Signup and view all the answers

What is the general formula for sin(180° ± θ)?

<p>± sin θ (A)</p> Signup and view all the answers

In which quadrant is the sine function positive?

<p>Quadrant II only (C)</p> Signup and view all the answers

What is the general solution for the equation (\tan \theta = x) in degrees?

<p>(\theta = \tan^{-1} x + k \cdot 180^\circ) (B)</p> Signup and view all the answers

In which quadrants are the cosine and tangent functions both positive?

<p>Quadrant I only (B)</p> Signup and view all the answers

What is the general solution for the equation (\cos \theta = x) in degrees?

<p>(\theta = \cos^{-1} x + k \cdot 360^\circ) or (\theta = 360^\circ - \cos^{-1} x + k \cdot 360^\circ) (B)</p> Signup and view all the answers

In which quadrants are the sine and cosine functions both negative?

<p>Quadrant III and Quadrant IV (A)</p> Signup and view all the answers

What is the first step in solving a trigonometric equation?

<p>Use a calculator to find the reference angle. (D)</p> Signup and view all the answers

What is the formula for the area of a triangle ABC in terms of side a and angle C?

<p>Area of triangle ABC = 1/2 ac sin C (A)</p> Signup and view all the answers

Which trigonometric identity is useful for solving triangles when we know two sides and the included angle?

<p>The Cosine Rule (B)</p> Signup and view all the answers

What is the purpose of the CAST diagram in solving trigonometric equations?

<p>To determine the quadrants where the trigonometric function is positive or negative (C)</p> Signup and view all the answers

What is the formula for the sine rule?

<p>sin A / a = sin B / b = sin C / c (A)</p> Signup and view all the answers

What is the general solution to a trigonometric equation?

<p>The solution within the interval [0°; 360°] plus multiples of the period (D)</p> Signup and view all the answers

What is the formula for the cosine rule in terms of side a and angle A?

<p>a^2 = b^2 + c^2 - 2bc cos A (C)</p> Signup and view all the answers

When solving a trigonometric equation, what is the purpose of checking the solution using a calculator?

<p>To ensure the solution satisfies the original equation (D)</p> Signup and view all the answers

What is the formula for the area of a triangle ABC in terms of side b and angle A?

<p>Area of triangle ABC = 1/2 bc sin A (C)</p> Signup and view all the answers

When solving a quadratic trigonometric equation, what is the first step?

<p>Simplify the equation and determine the reference angle (C)</p> Signup and view all the answers

What is the main advantage of using trigonometric identities?

<p>To simplify complex trigonometric expressions (D)</p> Signup and view all the answers

Which of the following is NOT a step in proving an identity?

<p>Differentiate both sides of the equation with respect to theta (D)</p> Signup and view all the answers

What is the value of sin^2 θ + cos^2 θ?

<p>1 (A)</p> Signup and view all the answers

Why is tan θ undefined when θ = k × 90°, where k is an odd integer?

<p>Because cos θ is zero (C)</p> Signup and view all the answers

What is the alternative form of the square identity sin^2 θ + cos^2 θ = 1?

<p>sin^2 θ = 1 - cos^2 θ (B), cos^2 θ = 1 - sin^2 θ (D)</p> Signup and view all the answers

What is the main purpose of the quotient identity?

<p>To express tangent in terms of sine and cosine (A)</p> Signup and view all the answers

What is the benefit of using the quotient identity?

<p>It allows us to express tangent in terms of sine and cosine (B)</p> Signup and view all the answers

What is the condition for the quotient identity to be defined?

<p>θ ≠ k × 90°, where k is an odd integer (A)</p> Signup and view all the answers

What is the condition under which the quotient identity tan θ = sin θ / cos θ is defined?

<p>cos θ ≠ 0 (B)</p> Signup and view all the answers

Which of the following is a result of the square identity?

<p>sin^2 θ + cos^2 θ = 1 (C)</p> Signup and view all the answers

What is the value of sin(180° + θ)?

<p>-sin θ (D)</p> Signup and view all the answers

If points P and P' are symmetrical about the y-axis, what is the coordinate of P' if P is (x, y)?

<p>(-x, y) (A)</p> Signup and view all the answers

What is the purpose of replacing 1 with sin^2 θ + cos^2 θ in trigonometric expressions?

<p>To simplify the expression (C)</p> Signup and view all the answers

What is the value of tan(180° - θ)?

<p>-tan θ (B)</p> Signup and view all the answers

What is the result of using the square identity to simplify sin^2 θ + cos^2 θ?

<p>1 (A)</p> Signup and view all the answers

What is the purpose of multiplying by a suitable fraction to simplify a trigonometric expression?

<p>To simplify the expression (A)</p> Signup and view all the answers

What is the value of sin(360° + θ)?

<p>sin θ (C)</p> Signup and view all the answers

If points P and P' are symmetrical about the y-axis, what are the coordinates of P'?

<p>(-x, y) (B)</p> Signup and view all the answers

What is the value of cos(90° + θ)?

<p>-sin θ (D)</p> Signup and view all the answers

What is the value of tan(180° + θ)?

<p>tan θ (C)</p> Signup and view all the answers

What is the value of sin(-θ)?

<p>-sin θ (B)</p> Signup and view all the answers

What is the relationship between sin(90° - θ) and cos θ?

<p>sin(90° - θ) = cos θ (C)</p> Signup and view all the answers

What is the value of cos(360° - θ)?

<p>cos θ (A)</p> Signup and view all the answers

How can cos 54° be expressed as a trigonometric ratio of 36°?

<p>cos 54° = sin 36° (B)</p> Signup and view all the answers

What is the general formula for sin(180° ± θ)?

<p>sin(180° ± θ) = -sin θ (B)</p> Signup and view all the answers

What is the value of tan(90° - θ)?

<p>tan θ (D)</p> Signup and view all the answers

In which quadrants is the tangent function positive?

<p>Quadrant I and Quadrant III (D)</p> Signup and view all the answers

What is the general solution for the equation (\sin \theta = x) in degrees?

<p>Both (\theta = \sin^{-1} x + k \cdot 360^\circ) and (\theta = 180^\circ - \sin^{-1} x + k \cdot 360^\circ) (B)</p> Signup and view all the answers

What is the general solution for the equation (\cos \theta = x) in degrees?

<p>Both (\theta = \cos^{-1} x + k \cdot 360^\circ) and (\theta = 360^\circ - \cos^{-1} x + k \cdot 360^\circ) (B)</p> Signup and view all the answers

In which quadrant is the cosine function positive?

<p>Quadrant I and Quadrant IV (C)</p> Signup and view all the answers

What is the purpose of the identities and rules in trigonometry?

<p>To simplify trigonometric expressions and evaluate trigonometric functions. (C)</p> Signup and view all the answers

What is the general solution for the equation (\tan \theta = x) in degrees?

<p>(\theta = \tan^{-1} x + k \cdot 180^\circ) (B)</p> Signup and view all the answers

Which trigonometric rule is used to find the area of a triangle when no perpendicular height is given?

<p>Area rule (A)</p> Signup and view all the answers

What is the first step in solving a trigonometric equation?

<p>Simplify the equation and determine the reference angle. (A)</p> Signup and view all the answers

Which trigonometric identity is used to express trigonometric functions in terms of acute angles?

<p>Reduction formula (D)</p> Signup and view all the answers

What is the purpose of the CAST diagram in solving trigonometric equations?

<p>To determine the quadrants where the trigonometric function is positive or negative. (C)</p> Signup and view all the answers

What is the formula for the sine rule?

<p>c/ cosC = b/ cosB = a/ cosA (D)</p> Signup and view all the answers

What is the general solution to a trigonometric equation?

<p>The solution is the angle that satisfies the equation plus multiples of the period. (D)</p> Signup and view all the answers

Which trigonometric rule is used to find the side of a triangle when two sides and the included angle are given?

<p>Cosine rule (B)</p> Signup and view all the answers

What is the purpose of checking the solution using a calculator in solving trigonometric equations?

<p>To ensure the solution satisfies the original equation. (D)</p> Signup and view all the answers

What is the formula for the cosine rule in terms of side a and angle A?

<p>a^2 = b^2 + c^2 - 2bc cosA (C)</p> Signup and view all the answers

In which quadrants is the tangent function positive?

<p>Quadrant III only (D)</p> Signup and view all the answers

What is the general solution for the equation sin θ = x?

<p>θ = sin⁻¹ x + k ⋅ 360° or θ = 180° - sin⁻¹ x + k ⋅ 360° (D)</p> Signup and view all the answers

In which quadrants are both the sine and cosine functions negative?

<p>Quadrant III and Quadrant IV (B)</p> Signup and view all the answers

What is the general solution for the equation tan θ = x?

<p>θ = tan⁻¹ x + k ⋅ 90° (D)</p> Signup and view all the answers

In which quadrants is the cosine function positive?

<p>Quadrant I and Quadrant IV (A)</p> Signup and view all the answers

What is the general solution for the equation cos θ = x?

<p>θ = cos⁻¹ x + k ⋅ 360° or θ = 360° - cos⁻¹ x + k ⋅ 360° (A)</p> Signup and view all the answers

In which quadrants is the sine function negative?

<p>Quadrant III and Quadrant IV (B)</p> Signup and view all the answers

What is the purpose of the CAST diagram in trigonometry?

<p>To identify the quadrants in which trigonometric functions are positive or negative (B)</p> Signup and view all the answers

What is the general formula for the solution of a trigonometric equation?

<p>θ = f⁻¹ x + k ⋅ 360° (D)</p> Signup and view all the answers

In which quadrants are both the sine and tangent functions positive?

<p>Quadrant I only (D)</p> Signup and view all the answers

What is the trigonometric identity that can be derived using the Pythagorean theorem?

<p>sin^2 θ + cos^2 θ = 1 (C)</p> Signup and view all the answers

Why is it necessary to change all trigonometric ratios to sine and cosine when proving an identity?

<p>To ensure all trigonometric ratios are in the same form (C)</p> Signup and view all the answers

What is the result of simplifying the expression (y/r) / (x/r) in terms of sine and cosine?

<p>sin θ / cos θ (D)</p> Signup and view all the answers

What is the advantage of using trigonometric identities when solving equations?

<p>It allows us to simplify the expression and solve the equation more easily (D)</p> Signup and view all the answers

What is the result of simplifying the expression (y^2 + x^2) / r^2 in terms of sine and cosine?

<p>sin^2 θ + cos^2 θ (D)</p> Signup and view all the answers

What is the purpose of proving trigonometric identities?

<p>To simplify trigonometric expressions (C)</p> Signup and view all the answers

What is the result of simplifying the expression sin^2 θ + cos^2 θ in terms of sine and cosine?

<p>1 (C)</p> Signup and view all the answers

Why is it usually better to choose the more complicated side of the equation to simplify when proving an identity?

<p>To ensure that the identity is true for all values of θ (C)</p> Signup and view all the answers

If point P has coordinates (√3, 1), what are the coordinates of P' if P and P' are symmetrical about the y-axis?

<p>(-√3, 1) (D)</p> Signup and view all the answers

What is the value of sin(360° + θ)?

<p>sin θ (D)</p> Signup and view all the answers

If points P and P' are symmetrical about the line y = x, what are the coordinates of P'?

<p>(y, x) (B)</p> Signup and view all the answers

What is the reduction formula for cos(90° + θ)?

<p>-cos θ (D)</p> Signup and view all the answers

What is the value of cos(180° - θ)?

<p>-cos θ (B)</p> Signup and view all the answers

If points P and P' are symmetrical about the x-axis, what is the value of sin(θ) in terms of P'?

<p>-sin θ (D)</p> Signup and view all the answers

What is the reduction formula for tan(90° + θ)?

<p>-tan θ (A)</p> Signup and view all the answers

What is the value of sin(180° + θ)?

<p>-sin θ (C)</p> Signup and view all the answers

What is the relationship between cos(90° - θ) and sin θ?

<p>cos(90° - θ) = sin θ (D)</p> Signup and view all the answers

What is the value of tan(360° - θ)?

<p>-tan θ (C)</p> Signup and view all the answers

What is the purpose of using the identity sin^2 θ + cos^2 θ = 1 in simplifying trigonometric expressions?

<p>To make the simplification process easier and more efficient. (D)</p> Signup and view all the answers

What is the correct form of the reduction formula for tan(180° - θ)?

<p>tan(180° - θ) = -tan θ (A)</p> Signup and view all the answers

What is the result of multiplying both sides of the equation by a suitable fraction, such as 1 + sin θ/1 + sin θ?

<p>The equation becomes simpler and easier to solve. (B)</p> Signup and view all the answers

What is the purpose of using the square root sign in trigonometric expressions?

<p>To indicate that the expression needs to be simplified. (C)</p> Signup and view all the answers

What is the result of replacing 1 with sin^2 θ + cos^2 θ in a trigonometric expression?

<p>The expression becomes simpler and easier to solve. (A)</p> Signup and view all the answers

What is the purpose of using the quotient identity in trigonometry?

<p>To simplify trigonometric expressions. (D)</p> Signup and view all the answers

What is the condition under which the quotient identity tan θ = sin θ/cos θ is defined?

<p>cos θ ≠ 0 (D)</p> Signup and view all the answers

What is the result of adding sin^2 θ to both sides of the equation sin θ = 1?

<p>The equation becomes simpler and easier to solve. (B)</p> Signup and view all the answers

What is the general solution for the equation sinθ = x in degrees?

<p>θ = sin^(-1) x + k · 360^° (B), θ = 90^° - sin^(-1) x + k · 360^° (C)</p> Signup and view all the answers

In which quadrant is the cosine function positive?

<p>Quadrant I and Quadrant IV (C)</p> Signup and view all the answers

What is the general solution for the equation tanθ = x in degrees?

<p>θ = tan^(-1) x + k · 180^° (A)</p> Signup and view all the answers

In which quadrant is the sine function negative?

<p>Quadrant III and Quadrant IV (B)</p> Signup and view all the answers

What is the general solution for the equation cosθ = x in degrees?

<p>θ = 360^° - cos^(-1) x + k · 360^° (B), θ = cos^(-1) x + k · 360^° (D)</p> Signup and view all the answers

What is the value of sin(90° - θ) cos(90° + θ) tan θ?

<p>-sin^2 θ (A)</p> Signup and view all the answers

If tan θ = 5, what is the value of θ in the first quadrant?

<p>arctan(5) (B), tan^(-1)(5) (C)</p> Signup and view all the answers

What is the general solution to the equation sin θ = 1/2?

<p>30° + 180°k (C), 30° + 360°k (D)</p> Signup and view all the answers

What is the formula for the area of a triangle ABC in terms of side a and angle B?

<p>1/2 ac sin B (D)</p> Signup and view all the answers

What is the purpose of the CAST diagram in solving trigonometric equations?

<p>To determine the quadrants where the trigonometric function is positive or negative (C)</p> Signup and view all the answers

What is the formula for the cosine rule in terms of side a and angle B?

<p>b^2 = a^2 + c^2 - 2ac cos B (B)</p> Signup and view all the answers

When solving a quadratic trigonometric equation, what is the first step?

<p>Simplify the equation (B)</p> Signup and view all the answers

What is the general solution to the equation tan θ = x in degrees?

<p>tan^(-1)(x) + 360°k (B), arctan(x) + 360°k (C)</p> Signup and view all the answers

Which trigonometric identity is useful for solving triangles when we know two sides and the included angle?

<p>Cosine rule (C)</p> Signup and view all the answers

What is the formula for the sine rule?

<p>sin A/a = sin B/b (D)</p> Signup and view all the answers

In which quadrant is the tangent function positive?

<p>Quadrant III (C)</p> Signup and view all the answers

What is the general solution to the equation ( \sin \theta = x ) in degrees?

<p>( \theta = \sin^{-1} x + k \cdot 360^\circ ) (C)</p> Signup and view all the answers

Which of the following trigonometric functions is positive in Quadrant II?

<p>Sine only (C)</p> Signup and view all the answers

What is the general solution to the equation ( \cos \theta = x ) in degrees?

<p>( \theta = \cos^{-1} x + k \cdot 360^\circ ) (D)</p> Signup and view all the answers

In which quadrant are the sine and tangent functions both positive?

<p>Quadrant I (A)</p> Signup and view all the answers

What is the implication of the square identity sin^2 θ + cos^2 θ = 1?

<p>All trigonometric identities can be derived from this identity (A)</p> Signup and view all the answers

If sin(180° - θ) = sin θ, what can be said about the angle 180° - θ?

<p>It is symmetrical about the y-axis (B)</p> Signup and view all the answers

What is the purpose of using the identity sin^2 θ + cos^2 θ = 1 in simplifying trigonometric expressions?

<p>To simplify the expression by reducing the number of terms (B)</p> Signup and view all the answers

If tan θ = -tan(180° - θ), what can be said about the angle 180° - θ?

<p>It is symmetrical about the y-axis (B)</p> Signup and view all the answers

What is the implication of the quotient identity tan θ = sin θ / cos θ?

<p>tan θ is undefined when cos θ = 0 (C)</p> Signup and view all the answers

If cos(180° + θ) = -cos θ, what can be said about the angle 180° + θ?

<p>It is symmetrical about the y-axis (B)</p> Signup and view all the answers

What is the purpose of using the reduction formula for sin(180° - θ)?

<p>To simplify trigonometric expressions (B)</p> Signup and view all the answers

What is the implication of the identity sin^2 θ = 1 - cos^2 θ?

<p>sin θ and cos θ are related by a quadratic equation (D)</p> Signup and view all the answers

What is the value of cos(360° + θ)?

<p>cos θ (A)</p> Signup and view all the answers

If P has coordinates (√3, 1), what are the coordinates of P' if P and P' are symmetrical about the line y = x?

<p>(1, √3) (D)</p> Signup and view all the answers

What is the value of sin(90° + θ)?

<p>cos θ (C)</p> Signup and view all the answers

If points P and P' are symmetrical about the x-axis, what is the value of tan(360° - θ)?

<p>-tan θ (B)</p> Signup and view all the answers

What is the value of cos(-θ)?

<p>cos θ (B)</p> Signup and view all the answers

What is the value of sin(180° - θ)?

<p>sin θ (A)</p> Signup and view all the answers

If points P and P' are symmetrical about the origin, what are the coordinates of P' if P has coordinates (√3, 1)?

<p>(-√3, -1) (A)</p> Signup and view all the answers

What is the value of sin(360° - θ)?

<p>-sin θ (C)</p> Signup and view all the answers

What is the value of cos(90° - θ)?

<p>sin θ (A)</p> Signup and view all the answers

What is the value of tan(180° + θ)?

<p>-tan θ (B)</p> Signup and view all the answers

What is the first step in solving a trigonometric equation when no interval is given?

<p>Determine the general solution using the periodicity of trigonometric functions. (C)</p> Signup and view all the answers

What is the formula for the area of a triangle ABC in terms of side c and angle B?

<p>1/2 ac sin B (C)</p> Signup and view all the answers

Which trigonometric identity is useful for solving triangles when we know two angles and a side?

<p>The Sine Rule (A)</p> Signup and view all the answers

What is the purpose of using the CAST diagram in solving trigonometric equations?

<p>To identify the quadrants where the trigonometric function is positive or negative (C)</p> Signup and view all the answers

What is the formula for the cosine rule in terms of side a and angle B?

<p>a^2 = b^2 + c^2 - 2ac cos B (D)</p> Signup and view all the answers

When solving a quadratic trigonometric equation, what is the first step?

<p>Simplify the equation using reduction formulae (A)</p> Signup and view all the answers

What is the main advantage of using trigonometric identities?

<p>They allow us to simplify trigonometric expressions (A)</p> Signup and view all the answers

What is the general solution to a trigonometric equation in degrees?

<p>θ + 360°k, where k is an integer (A)</p> Signup and view all the answers

Which trigonometric identity is useful for solving triangles when we know two sides and the included angle?

<p>The Cosine Rule (B)</p> Signup and view all the answers

What is the purpose of checking the solution using a calculator when solving a trigonometric equation?

<p>To ensure the solution satisfies the original equation (A)</p> Signup and view all the answers

If sin θ = 3/5, what is the value of cos θ?

<p>4/5 (D)</p> Signup and view all the answers

What is the value of tan θ if sin θ = 2/3 and cos θ = 1/3?

<p>3/2 (B)</p> Signup and view all the answers

If tan θ = 5/12, what is the value of sin θ?

<p>5/13 (B)</p> Signup and view all the answers

What is the value of cos^2 θ if sin θ = 3/5?

<p>16/25 (A)</p> Signup and view all the answers

If cos θ = 2/5, what is the value of tan θ?

<p>3/4 (D)</p> Signup and view all the answers

What is the value of sin^2 θ + cos^2 θ if sin θ = 3/5 and cos θ = 4/5?

<p>25/25 (B)</p> Signup and view all the answers

If tan θ = 3/5, what is the value of cos θ?

<p>4/5 (C)</p> Signup and view all the answers

What is the value of sin θ if cos θ = 3/5 and tan θ = 4/3?

<p>4/5 (C)</p> Signup and view all the answers

In which quadrant is the cosine function negative?

<p>Quadrant III (A)</p> Signup and view all the answers

What is the general solution for the equation ( \sin \theta = x ) in degrees?

<p>( \theta = 180^\circ - \sin^{-1} x + k \cdot 360^\circ ) (B), ( \theta = \sin^{-1} x + k \cdot 360^\circ ) (D)</p> Signup and view all the answers

In which quadrant are the sine and tangent functions both positive?

<p>Quadrant I (C)</p> Signup and view all the answers

What is the general solution for the equation ( \cos \theta = x ) in degrees?

<p>( \theta = \cos^{-1} x + k \cdot 360^\circ ) (B), ( \theta = 360^\circ - \cos^{-1} x + k \cdot 360^\circ ) (C)</p> Signup and view all the answers

In which quadrant is the tangent function negative?

<p>Quadrant I and Quadrant III (B)</p> Signup and view all the answers

What is the general solution for the equation ( \tan \theta = x ) in degrees?

<p>( \theta = \tan^{-1} x + k \cdot 180^\circ ) or ( \theta = 180^\circ - \tan^{-1} x + k \cdot 180^\circ ) (D)</p> Signup and view all the answers

In which quadrant are the sine and cosine functions both positive?

<p>Quadrant I (C)</p> Signup and view all the answers

What is the general solution for the equation ( \sin \theta = x ) in degrees if ( \theta ) is in the second quadrant?

<p>( \theta = 180^\circ - \sin^{-1} x ) (C)</p> Signup and view all the answers

In which quadrant is the sine function negative?

<p>Quadrant III and Quadrant IV (A)</p> Signup and view all the answers

What is the general solution for the equation ( \cos \theta = x ) in degrees if ( \theta ) is in the fourth quadrant?

<p>( \theta = 360^\circ - \cos^{-1} x ) (A)</p> Signup and view all the answers

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