Post on 16-Jul-2020
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