Compound & Double Angle Identities (Grade 12) — Worksheet & Memo

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Grade 12 · Trigonometry

Compound & Double Angle Identities (Grade 12)

MEMORANDUM

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Class:

Date:

Mark

/ 20

Answer all questions. Show all your working — marks are awarded for method as well as the final answer. Teacher copy: accept any correct equivalent method.

1
Expand cos(A − B).
(2)
cosA cosB + sinA sinB✓✓ (2)
2
Expand sin(A + B).
(2)
sinA cosB + cosA sinB✓✓ (2)
3
Determine the exact value of cos75° without a calculator.
(2)
cos(45°+30°) = 6 − 24✓✓ (2)
4
Determine the exact value of sin15° without a calculator.
(2)
sin(45°−30°) = 6 − 24✓✓ (2)
5
Write down the three forms of cos2A.
(2)
cos²A − sin²A, 2cos²A − 1, 1 − 2sin²A✓✓ (2)
6
If sinθ = 35 and θ is acute, determine cos2θ.
(2)
1 − 2(925) = 725✓✓ (2)
7
If sinθ = 35 and θ is acute, determine sin2θ.
(2)
cosθ = 45, so 2(35)(45) = 2425✓✓ (2)
8
Prove that sin2A1 + cos2A = tanA
(2)
2sinAcosA2cos²A = sinAcosA = tanA✓✓ (2)
9
Simplify 2 sin15° cos15°.
(2)
= sin30° = 12✓✓ (2)
10
Why is sin(A + B) ≠ sinA + sinB?
(2)
Test A = 30°, B = 60°: sin90° = 1 but sin30° + sin60° ≈ 1,37, so they are not equal.✓✓ (2)

TOTAL: 20 marks