Back to Topic 3.10 — Compound angles (HL only)
3.10.1Math AA HL8 flashcards

Compound angle identities

Practice Flashcards

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Card 1 of 83.10.1
3.10.1
Question

Expand sin(A + B).

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All 8 Flashcards — Compound angle identities

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Card 1formula

Question

Expand sin(A + B).

Answer

sin A cos B + cos A sin B (same sign as the bracket; terms cross over).

Card 2formula

Question

Expand cos(A − B).

Answer

cos A cos B + sin A sin B (terms match up; the middle sign FLIPS, so a − bracket gives a +).

Card 3concept

Question

Why does cos(A + B) have a MINUS in the middle?

Answer

The cos formula always flips the middle sign relative to the bracket: cos(A+B) = cos A cos B − sin A sin B.

Card 4formula

Question

Expand tan(A + B).

Answer

(tan A + tan B)/(1 − tan A tan B). The bottom sign is the opposite of the top.

Card 5formula

Question

State tan 2A and where it comes from.

Answer

tan 2A = 2 tan A/(1 − tan²A); put B = A in tan(A+B).

Card 6concept

Question

Find sin 75° exactly.

Answer

sin(45°+30°) = (√6 + √2)/4.

Card 7concept

Question

Find tan 75° exactly.

Answer

tan(45°+30°) = (√3+1)/(√3−1) = 2 + √3 after rationalising.

Card 8concept

Question

How do you SOLVE an equation like sin(x + π/6) = cos x?

Answer

Expand the bracket with sin(A+B), gather terms into one ratio (here tan x = 1/√3), then list all solutions in the interval.

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