Double Angle Identities

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Show your work for each problem.

1.
What is the double angle formula for sine?
1. a)
2. b)
3. c)
4. d)
2.
Which of the following is NOT a valid form of ?
1. a)
2. b)
3. c)
4. d)
3.
Calculate using the double angle formula with . Give your answer as a decimal rounded to 3 decimal places.
4.
Simplify . Give your exact answer as a decimal rounded to 3 decimal places.
5.
If and is in Quadrant I, what is ?
1. a)
2. b)
3. c)
4. d)
6.
If and is in Quadrant IV, find . Give your answer as a fraction in the form a/b.
7.
What is the double angle formula for tangent?
1. a)
2. b)
3. c)
4. d)
8.
Find if and is in Quadrant I.
9.
Derive the formula from .
10.
Calculate if . Give your answer as a fraction in the form a/b.
11.
Solve for .
12.
Find if and is in Quadrant III.
13.
At what angle does the projectile range formula give maximum range?
1. a)
2. b)
3. c)
4. d)
14.
Simplify using the double angle identity. Write your answer in terms of .
15.
Use the power-reducing identity to express in terms of .