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