Download 2 = 2cos 2 θ −1= 1−2 sin 2 θ = 1 + cosu 2 1− cosu 2

TRIGONOMETRY
1. a)
Half Angle Formulas
NAME____________________
Date__________Per.________
Which double angle equals these three formulas?
(cosθ )2 − (sinθ )2 = 2 cos2 θ − 1 = 1− 2 sin2 θ =
b) Let u = 2θ. Then dividing both sides by 2, θ =
Substitute θ = u/2 in part 1b) into the double angle formula that only has “cos” in it. so that x is the only
variable.
2. a)
b) Add 1 to
cos(2θ) = cos(u) =
both sides
=
c) Divide both
sides by 2
=
d) Take the square
root of both sides:
=
3. a)
Substitute the identities in part 1b) into the double angle formula that only has “sin” in it. so that u is the
only variable.
cos(2θ) = cos(u) =
c) Subtract 1
from both sides
=
d) Divide both
sides by -2
=
e) Take the square
root of both sides:
4.
+
1 + cosu
=
2
=
+ 1 − cos u
2
=