Theta in Trigonometry

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Questions and Answers

What does the Greek letter theta (θ) represent in trigonometry?

  • An angle in trigonometry (correct)
  • A trigonometric function
  • A side of a triangle
  • The radius of a circle

What is the definition of sine (sin) in terms of the sides of a right triangle?

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

What is the Pythagorean Identity in trigonometry?

  • sin^2(θ) + cos^2(θ) = 0
  • sin^2(θ) - cos^2(θ) = 1
  • tan^2(θ) + 1 = sec^2(θ)
  • sin^2(θ) + cos^2(θ) = 1 (correct)

What is the formula for the sine of the sum of two angles?

<p>sin(a + b) = sin(a)cos(b) + cos(a)sin(b) (C)</p> Signup and view all the answers

What is the Law of Cosines used for in trigonometry?

<p>To solve oblique triangles (C)</p> Signup and view all the answers

What is the unit circle used for in trigonometry?

<p>To define the trigonometric functions (B)</p> Signup and view all the answers

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Study Notes

Theta in Trigonometry

Definition

  • Theta (θ) is a Greek letter used to represent an angle in trigonometry
  • It is often used as the variable in trigonometric functions such as sine, cosine, and tangent

Unit Circle

  • The unit circle is a circle with a radius of 1 unit
  • Theta is used to measure the angle of rotation from the positive x-axis to a point on the unit circle
  • The unit circle is used to define the trigonometric functions sine, cosine, and tangent

Trigonometric Functions

  • Sine (sin): sin(θ) = opposite side / hypotenuse
  • Cosine (cos): cos(θ) = adjacent side / hypotenuse
  • Tangent (tan): tan(θ) = opposite side / adjacent side

Identities

  • Pythagorean Identity: sin^2(θ) + cos^2(θ) = 1
  • Sum and Difference Formulas:
    • sin(a + b) = sin(a)cos(b) + cos(a)sin(b)
    • cos(a + b) = cos(a)cos(b) - sin(a)sin(b)
    • tan(a + b) = (tan(a) + tan(b)) / (1 - tan(a)tan(b))

Solving Triangles

  • Theta is used to find the missing sides and angles of right triangles
  • Law of Sines: a / sin(A) = b / sin(B) = c / sin(C)
  • Law of Cosines: a^2 = b^2 + c^2 - 2bc cos(A)

Theta in Trigonometry

Definition of Theta

  • Theta (θ) is a Greek letter representing an angle in trigonometry
  • It's used as a variable in trigonometric functions like sine, cosine, and tangent

Unit Circle and Theta

  • The unit circle has a radius of 1 unit
  • Theta measures the angle of rotation from the positive x-axis to a point on the unit circle
  • The unit circle is used to define sine, cosine, and tangent functions

Trigonometric Functions and Theta

  • Sine (sin): ratio of opposite side to hypotenuse
  • Cosine (cos): ratio of adjacent side to hypotenuse
  • Tangent (tan): ratio of opposite side to adjacent side

Trigonometric Identities

  • Pythagorean Identity: sin^2(θ) + cos^2(θ) = 1
  • Sum and Difference Formulas:
    • sin(a + b) = sin(a)cos(b) + cos(a)sin(b)
    • cos(a + b) = cos(a)cos(b) - sin(a)sin(b)
    • tan(a + b) = (tan(a) + tan(b)) / (1 - tan(a)tan(b))

Solving Triangles with Theta

  • Theta is used to find missing sides and angles in right triangles
  • Law of Sines: a / sin(A) = b / sin(B) = c / sin(C)
  • Law of Cosines: a^2 = b^2 + c^2 - 2bc cos(A)

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