Theta in Trigonometry

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)

Understand the concept of theta in trigonometry, its definition, and its role in the unit circle and trigonometric functions.