Trig #4 Done.notebook
May 14, 2015
Pythagorean Identities:
sin2θ + cos2θ = 1
Trig Identities
Name: _________________
The other two Pythagorean Identities can be easily derived from the
one above.
Reciprocal Identities:
sinθ = 1
cscθ = 1
cscθ
cosθ = 1
sinθ
secθ = 1
secθ
tanθ = 1
-Divide the above equation by cos2θ:
cosθ
cotθ = 1
cotθ
tanθ
Quotient Identities:
tanθ =sinθ
cotθ = cosθ
cosθ
-Divide the above equation by sin2θ:
sinθ
Opposite Angle Identities:
sin(-θ) = -sinθ
cos(-θ) = cosθ
Cofunction Identities:
sin(π/2 - θ) = cosθ
cos(π/2 - θ) = sinθ
tan(-θ) = -tanθ
tan(π/2 - θ) = cotθ
Simplifying Expressions : Simplify the trig expressions using the
fundamental identities.
5.) sin(π/2 - θ)cscθ
1.) sinxcotx
6.) cosθ(1 + tan2θ)
2.) sinθcscθ
7.) csc 2x(1 - cos2x)
3.) cotα
cosα
4.) cos(-x)
sin(-x)
Trig #4 Done.notebook
May 14, 2015
Verifying Trig Identities: Verify the following identities.
4.) sin(π/2 - x)tanx = sinx
1.) sinxcscx = 1
2.) tanθcscθcosθ = 1
5.) sin2x + cos2x = sinx
cscx
3.) 2 - cos2θ = 1 + sin2θ
6.) tan2θ + 4 = sec2θ + 3