Trig Identities
Name: _________________
Reciprocal Identities:
sinθ = 1
cscθ = 1
cscθ
Objectives: Students will be able to verify and simplify
trig identities.
sinθ
cosθ = 1
secθ
secθ = 1
cosθ
tanθ = 1
cotθ
cotθ = 1
tanθ
Quotient Identities:
tanθ =sinθ
cotθ = cosθ
cosθ
sinθ
Opposite Angle Identities:
sin(-θ) = -sinθ
cos(-θ) = cosθ
Cofunction Identities:
sin(π/2 - θ) = cosθ
tan(-θ) = -tanθ
cos(π/2 - θ) = sinθ
tan(π/2 - θ) = cotθ
Apr 22­3:24 PM
Pythagorean Identities:
sin2θ + cos2θ = 1
The other two Pythagorean Identities can be easily derived from the
one above.
-Divide the above equation by cos2θ:
-Divide the above equation by sin2θ:
Apr 22­3:26 PM
1
Simplifying Expressions : Simplify the trig expressions using the
fundamental identities.
1.) sinxcotx
2.) sinθcscθ
3.) cotα
cos α
4.) cos(-x)
sin(-x)
Apr 22­3:35 PM
5.) sin(π/2 - θ)cscθ
6.) cos θ(1 + tan2θ)
7.) csc 2x(1 - cos2x)
Apr 22­3:47 PM
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Verifying Trig Identities: Verify the following identities.
1.) sinxcscx = 1
2.) tanθcscθcosθ = 1
3.) 2 - cos2θ = 1 + sin2θ
Apr 22­3:53 PM
4.) sin(π/2 - x)tanx = sinx
5.) sin2x + cos2x = sinx
cscx
6.) tan2θ + 4 = sec2θ + 3
Apr 22­4:01 PM
3
ICE
1.) Simplify sinxcosxtanxcotx.
2.) Verify that sin2x + 1 = 2 - cos2x.
Apr 26­8:43 AM
Solve Trig Equations
Objectives: Students will be able to solve trig equations.
Solve the trig equations on the interval 0 ≤θ<2π.
1.) 2sinx - 1 = 0
2.) 2cosx + √3 = 0
3.) sin2x - sinx = 0
Apr 22­5:18 PM
4
May 1­9:03 AM
Find the general solution of the equations.
4.) 2sinx - 2 = 0
5.) 3tanx - √3 = 0
6.) ½cosx = - sinxcosx
Apr 22­5:21 PM
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