May 02, 2016
Precalculus with Trigonometry
Section 7.4
Day 1
Objectives:
1. Use algebra to simplify trigonometric
expressions.
2. Establish Identities.
May 02, 2016
Reciprocal Identities
csc θ =
1 sec θ = 1
cot θ = 1
sin θ
cos θ
tan θ
Quotient Identities
tan θ = sin θ
cos θ
cot θ = cosθ
sin θ
May 02, 2016
Pythagorean Identities
sin2 θ + cos2 θ = 1
tan2 θ + 1 = sec2 θ
cot2 θ + 1 = csc2 θ
Even-Odd Identities
sin(-θ) = -sin θ
cos(-θ) = cos θ
tan(-θ) = -tan θ
csc(-θ) = - cscθ
sec(-θ) = sec θ
cot(-θ) = -cot θ
May 02, 2016
Use Algebraic Techniques to Simplify
The Trigonometric Expressions
Simplify by rewriting each trigonometric function in
terms of sine and cosine.
1.
2. cscθ tanθ
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3. secθ (secθ - cosθ)
4. sinθ (1 + cot2θ)
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5.
6.
7.
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8.
9.
10.
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11.
12.
13.
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14.
15.
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Homework:
WS 7.4 DAY 1