Sec 5.1 Simplifying Trig Expressions
Simplifying using the Trig Identities
1. cscx*sinx
2. (sin2(π/2 - x))/cosx
3. sec(90∘ -x)/cscx
4. sec2(π/2 -x)
sinx
5. sec2x - 1
1 - cos2x
6. cosu(secu - cosu)
7. sin2u sec2u + sinu cscu
8. (2sinx + sin(-x))/cos(-x)
9. sec2u -1
sec2u
Sec 5.1 Simplifying Trig Expressions
Factoring Trig Expressions
1.
csc 2x -1
cscx +1
2.
4tan2u + tanu -3
3.
cos2x sec 2x - cos 2x
4.
cot2x - cot 2x cos 2x
5.
sec 4u - tan 4u
6.
sin4x - 2sin2x + 1
7.
sec 2 + tanx - 13
Sec 5.1 Simplifying Trig Expressions
Rationalizing Trig Expressions
1.
1
1 + sinx
2.
sinu
1+cosu
+
cosu
sinu
Rewrite expression so it is not a fraction:
1. cos 2y
1-siny
2.
1
1 + sinx
Sec 5.1 Simplifying Trig Expressions
Use trig substitution to write as trig function of θ (0<θ<π/2)
1. √x2 - 25
x = 5secθ
Solve using graphing calculator if 0<θ<2π:
1.
cosθ = - √1-sin2θ
Express all trig functions in terms of cosθ:
sin2θ = 1- cos 2θ,
cscθ
secθ
tanθ
cotθ
so sinθ = ±√1-cos2θ