Trigonometry Worksheet Page 18
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22cos{2 { = cos
− sin
$
$
= {1 − sin
{ − sin
$
$
= 1 − 2 sin
$
In case (2), we substitute sin
with 1 − cos
$
$
and simplify:
cos{2 { = cos
− sin
$
$
= cos
− {1 − cos
{
$
$
= 2 cos
− 1
$
Homework Set
State the angle in degrees.
1. Initial side: positive x-axis, terminal side: negative x-axis, clockwise rotation.
2. Initial side: negative y-axis, terminal side: positive x-axis, counterclockwise rotation.
3. Initial side: positive y-axis, terminal side: positive y-axis, counterclockwise rotation.
4. Initial side: negative x-axis, terminal side: negative y-axis, clockwise rotation.
For the given angles, state (a) whether it is acute, obtuse or neither, (b) its supplement, (c) its
complement, if it is defined, and (d) its quadrant, if it is defined.
5. 43°
6. 71°
7. 120°
8. 235°
9. 90°
10. 180°
11. 35.26°
12. 174.18°
For the given angles, state its equivalent coterminal angle as described
13. 30°, negative rotation.
14. 41°, negative rotation.
15. 52°, one extra positive rotation.
16. 112°, one extra positive rotation.
17. 230°, one extra negative rotation.
18. 310°, one extra negative rotation.
19. 67.2°, two extra positive rotations.
20. 31.4°, three extra negative rotations.
21. A basketball makes 5 complete rotations between the time it is let go by the shooter and before
it enters the basket. How many degrees did the basketball turn while in the air?
22. A figure skater makes 8 complete rotations plus an extra half-rotation during part of her routine.
How many degrees did she rotate?
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