M5.3.7 For the adult
Compound and double angles
If I know sin A and sin B, how do I find sin(A + B), and why is it not sin A + sin B?
What this chapter teaches
The compound angle formulas give the sine, cosine and tangent of A + B or A − B from those of A and B. The key one is cos(A − B) = cos A cos B + sin A sin B, from the distance between two points on the unit circle. Putting B = A gives the double angle formulas, including three forms of cos 2A. These turn equations with 2x into equations in one trig function.
Three questions to ask
There is no one right wording. Listen for the idea.
- Why is sin(A + B) not equal to sin A + sin B when A = B = 90°?
- Which form of cos 2A would you use if the equation also contained sin x?
- How do the compound formulas give sin 75° exactly?
After the chapter, the learner can
- Use the formula for sin(A + B)
- Use double angle formulas to solve an equation
What they copy into their notebook
sin(A ± B) = sin A cos B ± cos A sin B. cos(A + B) = cos A cos B − sin A sin B. For A − B, use plus. sin 2A = 2 sin A cos A. cos 2A = 2cos²A − 1 = 1 − 2 sin²A.