∑ DANEMATHICS
FREE CAPS MATHS RESOURCES
Grade 12 · Trigonometry
Compound & Double Angle Identities (Grade 12)
EXAM-STYLE CLASS TEST
Marks
35
Duration
55 minutes
Questions
3
Name:
Class:
Date:
Mark
/ 35
Instructions and Information
- Answer ALL the questions in this question paper.
- Answer QUESTION 1 by circling the letter (A–D) in the answer grid at the end of that section.
- Show ALL calculations clearly.
- Show all units where applicable.
- Number the answers correctly according to the numbering system used in this question paper.
- A non-programmable calculator may be used, unless stated otherwise.
- Write neatly and legibly.
Question 1
[10 MARKS]Four options are given as possible answers to the following questions. Choose the correct answer and circle the letter (A–D) in the grid at the end of this section. If you want to change your choice, put a cross through the wrong letter and circle your new choice.
- 1.1sin(A + B) = …(1)A)sin A cos B + cos A sin BB)sin A cos B − cos A sin BC)cos A cos B − sin A sin BD)sin A + sin B
- 1.2cos(A + B) = …(1)A)cos A cos B − sin A sin BB)cos A cos B + sin A sin BC)sin A cos B + cos A sin BD)cos A + cos B
- 1.3sin 2θ = …(1)A)2 sin θ cos θB)2 sin θC)sin²θ + cos²θD)sin θ + cos θ
- 1.4Which is NOT one of the three forms of cos 2θ?(1)A)2 sin²θ − 1B)cos²θ − sin²θC)1 − 2 sin²θD)2 cos²θ − 1
- 1.5Using the double-angle formula on 30°, sin 60° = …(1)A)√32B)12C)√34D)1
- 1.6cos 2θ written in terms of cos θ only is …(1)A)2 cos²θ − 1B)1 − 2 cos²θC)cos²θ − 1D)2 cos²θ + 1
- 1.7If sin θ = 35 and θ is acute, then sin 2θ = …(1)A)2425B)65C)725D)1225
- 1.8For that same θ, cos 2θ = …(1)A)725B)2425C)1625D)−725
- 1.9sin 75° written as a compound angle is …(1)A)sin 45° cos 30° + cos 45° sin 30°B)sin 45° cos 30° − cos 45° sin 30°C)sin 45° + sin 30°D)cos 45° cos 30° − sin 45° sin 30°
- 1.10cos 15° cos 45° + sin 15° sin 45° = …(1)A)√32B)12C)√22D)cos 75°
Answer grid — circle your answers for Question 1
| 1.1 | A | B | C | D |
| 1.2 | A | B | C | D |
| 1.3 | A | B | C | D |
| 1.4 | A | B | C | D |
| 1.5 | A | B | C | D |
| 1.6 | A | B | C | D |
| 1.7 | A | B | C | D |
| 1.8 | A | B | C | D |
| 1.9 | A | B | C | D |
| 1.10 | A | B | C | D |
Question 2
[13 MARKS]Answer the questions below WITHOUT the use of a calculator.
- 2.1Determine the exact value of cos 15° using a compound-angle formula.(5)
- 2.2Simplify fully: sin 2A1 + cos 2A(4)
- 2.3Prove the identity: sin(A + B) − sin(A − B) = 2 cos A sin B(4)
Question 3
[12 MARKS]Answer the questions below.
- 3.1Write down the THREE forms of the identity for cos 2A.(3)
- 3.2If sin 25° = p, express sin 50° in terms of p.(4)
- 3.3Solve for x ∈ [0° ; 360°]: sin 2x = cos x(5)
TOTAL: 35 marks
This question paper consists of 3 questions.