1. DOUBLE- & HALF-ANGLE FORMULAS.
Double Angle or

2. DOUBLE- & HALF ANGLE FORMULAS cont’d

3. Ex. If sinA=12/13 and A is in the Quad. I, find each value.
1. cos2A
Formula: cos2A=1-2sin2A (There are 3 formulas for
this…sometimes one is more appropriate than the others…
here it won’t matter.) 13 12 A
cos2A=1-2(12/13)2
=1-2(144/169)
=1- (288/169)

4. Ex. If sinA=12/13 and A is in the Quad. I, find each value.2.
Formula:
(Note: the +or- depends
on which Quad. A/2 is in) 13
We need cos A (adj/hyp)…so use Pythag. Thm. to find b: 12
b=5 A b
= 5
& cos A=5/13
: Because we are Quad. I, we
know that the cosine is positive.

5. Ex. Use half-angle identity to find each value.3.
Formula:
(Note: the +or- depends
on which Quad. A/2 is in)
We need in Quad. III:
: Because we are Quad. III, we
know that the cosine is negative.

6. Ex. Verify that the following is an identity.4.
Hint:
…multiply by conjugate of denominator: