WArmup Rewrite 240° in radians.

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

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.

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

Hard way Identity way

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

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

Simplify each expression.

Simplify each expression.

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

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

Simplify each expression.

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

Simplify each expression.