Compound and Double Angles

Sine does not distribute.

10 problems · about 21 minutes · F-TF.C.9

NameDate

Figure — use these to answer the problems

Compare the angle at A with the angle at 2A. The coordinates are not doubled.

Angle in degrees30

Figure 1

From earlier lessons. Loosen up before the new work.

2 problems

From “Even, Odd, and Cofunction Identities”
sin θ = 0.9. What is sin(−θ)?
Answer
From “Proving an Identity”
What is sin²θ + cos²θ for any angle?
Answer

Straightforward practice. Get the method working first.

4 problems

sin A = 0.5 and cos A = 0.866. What is sin 2A, to two places?
Answer
4
Why is sin(A + B) not sin A + sin B?
- Sine is a function, not a multiplier, so it does not distribute.
- It is too hard to compute.
sin A = 0.8, cos A = 0.6. What is sin 2A?
Answer
cos A = 0.6, sin A = 0.8. What is cos 2A?
Answer

The same ideas with more to keep track of.

2 problems

Mixed problems. Work out what kind of question it is before you start.

2 problems