1. Trig. Identities Review
with Amir and Jimmy

2. What is an identity?
An identity is an equation that is always true for any value of the variable.
In this topic, there are five different identities.
Reciprocal Identities
Quotient Identities
Pythagorean Identities
Sum and Difference Identities
Double and Half-Angle Identities

3. Reciprocal Identities
These are identities that are made by putting the three trigonometric functions we learned about, sine, cosine and tangent under 1.
cosθ sinθ tanθ
= secθ
= cscθ
=cotθ

4. Quotient Identities
These identities provide an alternate way to finding tangent and cotangent.
sinθ
cosθ
tanθ =
cotθ =

5. Pythagorean Identities
A pythagorean identity is a trigonometric identity expressing the pythagorean theorem in terms of trigonometric functions.

6. How do you find a pythagorean identity?
If you represent a point on a right triangle in the unit circle with the coordinates (cosθ,sinθ) you can plug those coordinates into the pythagorean theorem equation and find the equation cos²θ+sin²θ=1.
This equation is called a pythagorean identity
and can be used to find other pythagorean
identities. 1
y=sinθ θ
x=cosθ

7. The 3 Pythagorean Identities
Using the first pythagorean identity, cos²θ+sin²θ=1, you can derive the two other pythagorean identities.
1st option: nd option:
cos²θ + sin²θ = cos²θ + sin²θ = 1
cos²θ cos²θ cos²θ sin²θ sin²θ sin²θ
1 + tan²θ = sec²θ cot²θ + 1 = csc²θ

8. Sum and Difference Identities
Sum and Difference Identities are equations that help you find the sine, cosine or tangent of the sum or difference of two given angles.
Cos(A∓B) = cos(A)✕cos(B) ∓ sin(A)✕cos(B)
Sin(A∓B) = sin(A)✕cos(B) ∓ cos(A)✕sin(B)
tan(A) ∓ tan(B)
1 ∓ tan(A)✕tan(B)
Tan(A∓B) =

9. Double and Half Angle Identities
Double-Angle and Half-Angle formulas are very useful for solving rational functions of sine and cosine. They are as follows:
sin2θ=2sinθcosθ sin1/2θ= cosθ
cos2θ=cos²θ-sin²θ
cos2θ=2cos²θ-1 cos1/2θ= 1+cosθ
cos2θ=1-2sin²θ
tan2θ=2tanθ tan1/2θ= cosθ
1-tan²θ cosθ ∓ ∓ ∓