Pre-Calculus II
5.3 – Double-Angle, Power-Reducing, and Half-Angle
Formulas
Double-Angle Formulas
1 |P a ge
Hannah Province – Mathematics Department – Southwest Tennessee Community College
Example – If
and θ lies in quadrant II, find the exact
value of each of the following:
a)
b)
c)
2 |P a ge
Hannah Province – Mathematics Department – Southwest Tennessee Community College
Example – Verify the identity:
3 |P a ge
Hannah Province – Mathematics Department – Southwest Tennessee Community College
Example – Find the exact value of
Example -
2 tan 22.50
Find the exact value of
1  tan 2 22.50
4 |P a ge
Hannah Province – Mathematics Department – Southwest Tennessee Community College
Power-Reducing Formulas
Write an equivalent expression for sin 4 x that does
Example -
not contain powers of trigonometric functions greater
than 1.
5 |P a ge
Hannah Province – Mathematics Department – Southwest Tennessee Community College
Half-Angle Formulas
6 |P a ge
Hannah Province – Mathematics Department – Southwest Tennessee Community College
Example –
Example -
Find the cos
5
1  5
. Use

8
2  4

.

7 |P a ge
Hannah Province – Mathematics Department – Southwest Tennessee Community College
Example –
Find the sin 750 using the sin
x
formula.
2
8 |P a ge
Hannah Province – Mathematics Department – Southwest Tennessee Community College
Example -
If tan  =-1 and  lies in quadrant II, find cos 2 .
9 |P a ge
Hannah Province – Mathematics Department – Southwest Tennessee Community College