Lesson 1verifying trig identities.notebook February 24, 2014
Unit 5 : Analytic Trigonometry
Test One: Verifying and Using Trig Identities
Fundamental IdentitiesQuotient Identities
tanθ=sinθcosθ
cotθ= sinθcosθ
Lesson 1verifying trig identities.notebook February 24, 2014
Reciprocal Identities
cscθ=sinθ
1
1cosθ
secθ=
tanθ1cotθ=
Lesson 1verifying trig identities.notebook February 24, 2014
Pythagorean Identities
sin2θ + cos2θ = 1
tan2θ + 1 = sec2θPythagorean Identities
Lesson 1verifying trig identities.notebook February 24, 2014
1 + cot2θ = csc2θPythagorean Identities
ExamplesVerify each trig identity.
cosθ(tanθ + cotθ) = cscθex 1)
Lesson 1verifying trig identities.notebook February 24, 2014
Verifying Trig Identities
1- Transform the more complicatedinto the simpler side
2- Substitute one or more basic identities
3- You may need to factor, add/subt. fractions,square a binomial, distribute, . . .
4- Multiply numerator & denominator by the same thing
Hints/Tips/Suggestions (but not steps!!)
5- Convert all terms to sin & cos
6- START OVER-- YOU ARE PROBABLY OVERTHINKING!!!
ex2) (secθ - 1)(secθ + 1) = tan2θ
Lesson 1verifying trig identities.notebook February 24, 2014
ex 3) cscθtanθ = secθ
ex 4) = tanθ
1 + tanθ
1 + cotθ
Lesson 1verifying trig identities.notebook February 24, 2014
ex 5)2cscθ
sinθ1 + cosθ
1 + cosθsinθ
=+
ex 6)
= 1tanθ + cotθsecθcscθ
Lesson 1verifying trig identities.notebook February 24, 2014
You Try:
tanθ = sinθcot2θ
cosθ
pg 3621119 odds
Lesson 1verifying trig identities.notebook February 24, 2014
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