Cogito
Integrated Math 3 · Chapter 6 · Lesson 2
Sum, Difference, and Double Angle
Sine does not distribute.
12 problems · about 22 minutes · F-TF.C.9
What this lesson teaches
The student applies sum, difference and double angle formulas.
- sin(A + B) is not sin A + sin B.
- Sine keeps the operation sign; cosine reverses it.
- Double angle formulas come from setting B equal to A.
Warm Up
Straightforward practice. Get the method working first.
5 problemssin A = 0.6 and cos A = 0.8. What is cos 2A?
Answer 0.28
Why 0.28.
Which formula reverses the sign between its products?
Answer The cosine sum and difference formulas.
Why Cosine reverses it.
sin A = 0.6, cos A = 0.8. What is sin 2A?
Answer 0.96
Why 2 sin A cos A.
Same values. What is cos 2A?
Answer 0.28
Why 0.64 − 0.36.
sin A = 0.5, cos A = 0.866. What is sin 2A, to three decimal places?
Answer 0.866
Why 2 × 0.5 × 0.866.
Build It Up
The same ideas with more to keep track of.
3 problems75° is the sum of 45° and which angle, in degrees?
Answer 30
Why 75 − 45.
In cos(A + B), what sign sits between the two products? 1 plus, 2 minus.
Answer 2
Why Cosine reverses the sign.
How many equivalent forms does cos 2A have?
Answer 3
Why Count them.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
4 problemsSort each formula by which sign it uses between the products.
Answer Keeps the operation sign: sin(A plus B), sin(A minus B) · Reverses the sign: cos(A plus B), cos(A minus B)
Why Only cosine reverses.
sin A = 0.8, cos A = 0.6. What is sin 2A?
Answer 0.96
Why 2 × 0.8 × 0.6.
The Test: Is sin(A + B) equal to sin A + sin B? 1 yes, 0 no.
Answer 0
Why No.
The Double: sin A = 0.6 and cos A = 0.8. What is sin 2A?
Answer 0.96
Why 0.96.