Untitled Quiz

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Questions and Answers

What is the correct definition of the sine function based on the right triangle definition?

sin(θ) = adjacent / hypotenuse
sin(θ) = opposite / adjacent
sin(θ) = opposite / hypotenuse (correct)
sin(θ) = hypotenuse / opposite

Which of the following statements correctly represents the domain of the tangent function?

θ can be any angle except 90 degrees
θ cannot equal nπ, where n is any integer
θ can be any angle
θ cannot equal n + π, where n is any integer (correct)

What is the period of the function cos(ωθ)?

2πω
2π
ω (correct)
π

What does the cosecant function equal in terms of sine?

csc(θ) = hypotenuse / opposite (D)

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Which of the following functions has the same periodicity as the sine function?

csc(θ) (D)

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What is the relationship between secant and cosine?

sec(θ) = 1 / cos(θ) (D)

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In terms of the unit circle, which coordinates correspond to the sine function?

(cos(θ), sin(θ)) (B)

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Which of the following is NOT defined for the cosecant function?

nπ where n is any integer (B)

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Which of the following statements about the range of the sine function is true?

The sine function ranges from -1 to 1. (C)

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Which identity correctly represents the relationship between tangent and cotangent?

tan(θ) = 1/cot(θ) (B)

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Which of the following ranges is correct for the cosecant function?

csc(θ) ≥ 1 and csc(θ) ≤ −1 (D)

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What is the correct expression to define tan(θ) using sine and cosine?

tan(θ) = sin(θ)/cos(θ) (B)

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The inverse function sin^(-1)(x) is defined for which domain?

−1 ≤ x ≤ 1 (D)

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What is the formula for the sine of a double angle?

sin(2θ) = 2sin(θ)cos(θ) (D)

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Which of the following statements about the periodic properties of sine is correct?

sin(θ + 2π) = sin(θ) (D)

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In which scenario is the cosecant function undefined?

When sin(θ) = 0 (B)

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What is the result of applying the Even/Odd formula to the cosine function?

cos(-θ) = cos(θ) (B)

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What is the domain of the function tan^(-1)(x)?

−∞ < x < ∞ (A)

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Which identity accurately describes the relationship between the cosine and sine of complementary angles?

Both B and C are correct. (B)

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Which of the following is not a Pythagorean identity?

tan²(θ) + 1 = cot²(θ) (B)

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Which of the following is the definition of the cosecant function?

csc(θ) = 1/sin(θ) (D)

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The formula for the secant function is derived from which basic function?

cos(θ) (A)

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Flashcards

Sine of an angle

In a right triangle, the ratio of the side opposite to the angle to the hypotenuse.

Cosine of an angle

In a right triangle, the ratio of the side adjacent to the angle to the hypotenuse.

Tangent of an angle

In a right triangle, the ratio of the side opposite to the angle to the side adjacent to the angle.

Period of a function

The number T such that f(θ + T) = f(θ) for any angle θ.

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Sin function domain

All angles.

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Cos function domain

All angles.

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Tan function domain

All angles except odd multiples of π/2.

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Period of Sin(ωθ)

2π/ω

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Range of sin(θ)

The range of the sine function is all values between -1 and 1, inclusive. -1 ≤ sin(θ) ≤ 1

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Range of cos(θ)

The range of the cosine function is all values between -1 and 1, inclusive. -1 ≤ cos(θ) ≤ 1

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Range of tan(θ)

The range of the tangent function is all real numbers. −∞ < tan(θ) < ∞

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Range of cot(θ)

The range of the cotangent function is all real numbers. −∞ < cot(θ) < ∞

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Range of sec(θ)

The range of the secant function includes values greater than or equal to 1, and less than or equal to -1. sec(θ) ≥ 1 and sec(θ) ≤ −1

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Range of csc(θ)

The range of the cosecant function includes values greater than or equal to 1, and less than or equal to -1. csc(θ) ≥ 1 and csc(θ) ≤ −1

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sin(θ) + sin(β)

Sum-to-product formula for sine adds to 2 sin((α+β)/2) cos((α-β)/2)

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cos(θ) + cos(β)

Sum-to-product formula for cosine adds to 2 cos((α+β)/2) cos((α-β)/2)

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sin(2θ)

Double angle formula; equal to 2sin(θ)cos(θ)

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cos(2θ)

Double angle formula; equal to cos²(θ) − sin²(θ) or 2cos²(θ) -1

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Periodicity of trig functions

Trigonometric functions repeat every 2π radians (or 360 degrees) for sine and cosine and every π radians (or 180 degrees) for tangent and cotangent.

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Untitled Quiz

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Questions and Answers

What is the correct definition of the sine function based on the right triangle definition?

Which of the following statements correctly represents the domain of the tangent function?

What is the period of the function cos(ωθ)?

What does the cosecant function equal in terms of sine?

Which of the following functions has the same periodicity as the sine function?

What is the relationship between secant and cosine?

In terms of the unit circle, which coordinates correspond to the sine function?

Which of the following is NOT defined for the cosecant function?

Which of the following statements about the range of the sine function is true?

Which identity correctly represents the relationship between tangent and cotangent?

Which of the following ranges is correct for the cosecant function?

What is the correct expression to define tan(θ) using sine and cosine?

The inverse function sin^(-1)(x) is defined for which domain?

What is the formula for the sine of a double angle?

Which of the following statements about the periodic properties of sine is correct?

In which scenario is the cosecant function undefined?

What is the result of applying the Even/Odd formula to the cosine function?

What is the domain of the function tan^(-1)(x)?

Which identity accurately describes the relationship between the cosine and sine of complementary angles?

Which of the following is not a Pythagorean identity?

Which of the following is the definition of the cosecant function?

The formula for the secant function is derived from which basic function?

Flashcards

Sine of an angle

Cosine of an angle

Tangent of an angle

Period of a function

Sin function domain

Cos function domain

Tan function domain

Period of Sin(ωθ)

Range of sin(θ)

Range of cos(θ)

Range of tan(θ)

Range of cot(θ)

Range of sec(θ)

Range of csc(θ)

sin(θ) + sin(β)

cos(θ) + cos(β)

sin(2θ)

cos(2θ)

Periodicity of trig functions

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