1. WArmup
Rewrite 240° in radians.

2. 13-1 Trig Identities Use trig identities to simplify expressions
Use trig identities to find trig values

3. Trig identity: an equation involving trig functions that is true for all values for which every expression in the equation is defined.
Just one counterexample is enough to prove an equation is NOT an identity.

4. Reciprocal identities
Basic trig identities that you already know:
Reciprocal identities
sin 𝜃 = 1 csc 𝜃 , csc 𝜃≠ csc 𝜃 = 1 sin 𝜃 , sin 𝜃≠0
cos 𝜃 = 1 sec 𝜃 , sec 𝜃≠ sec 𝜃 = 1 cos 𝜃 , cos 𝜃≠0
tan 𝜃 = 1 cot 𝜃 , cot 𝜃≠ cot 𝜃 = 1 tan 𝜃 , tan 𝜃≠0

5. Hard way
Identity way

6. Quotient Identities:
tan 𝜃 = sin 𝜃 cos 𝜃 , cos 𝜃≠0
cot 𝜃 = cos 𝜃 sin 𝜃 , sin 𝜃≠0

7. Pythagorean Identities:
𝑐𝑜𝑠 2 𝜃+ 𝑠𝑖𝑛 2 𝜃=1
𝑡𝑎𝑛 2 𝜃+1= 𝑠𝑒𝑐 2 𝜃
𝑐𝑜𝑡 2 𝜃+1= 𝑐𝑠𝑐 2 𝜃

8. Simplify each expression.

9. Simplify each expression.

10. Pos: sine Neg: cosine
cosecant secant
tangent
cotangent
Pos: ALL Neg: NONE
Pos: tangent Neg: sine
cotangent cosine
cosecant
secant
Pos: cosine Neg: sine
secant cosecant

11. Cofunction Identities: sin 𝜋 2 −𝜃 = cos 𝜃
cos 𝜋 2 −𝜃 = sin 𝜃
tan 𝜋 2 −𝜃 = cot 𝜃 ⁡ 𝜃

12. Simplify each expression.

13. Negative Angle Identities: sin −𝜃 =− sin 𝜃 cos −𝜃 = cos 𝜃
tan −𝜃 =− tan 𝜃
Even function
Odd function
Odd function

14. Simplify each expression.