Section 7.1: Trigonometric Identities

Pre­Calculus

November 19, 2015

7-1: Trigonometric Identities

Trigonometric Identity - any trig equation that is true for all values except those that make either side undefined

Reciprocal Identities

csc θ = 1 sin θ

sec θ = 1 cos θ

cot θ = 1 tan θ

Pythagorean Identites *Notation: sin2θ = (sin θ)2

sin2θ + cos2θ = 1 Why is this true? Use SOH-CAH-TOA!

1 + tan2θ = sec2θ

1 + cot2θ = csc2θ

Section 7.1: Trigonometric Identities

Pre­Calculus

November 19, 2015

Quotient Identities

tanθ = sinθ cotθ = cosθ cosθ sin θ

Why this works...

I. Transforming Identities

Since sin2θ + cos2θ = 1, then...

sin2θ =

cos2θ =

Section 7.1: Trigonometric Identities

Pre­Calculus

November 19, 2015

II. Finding Trig Values (between 0° & 90°)

1. If sec θ = 3/2, then cos θ =

2. If cot θ = 3/4, then the tan θ =

3. If csc θ = 4/3, find the tan θ

4. If the cos θ = 3/5, find the csc θ.

Section 7.1: Trigonometric Identities

Pre­Calculus

November 19, 2015

III. Using Trig Identities to Simplify

1. cscθtanθ 2. secθcosθ - cos2θ

3. cosθcscθ cotθ

4. sinx + cosxcotx