Special Angles, Reciprocal Ratios & Trig Equations (Grade 10)

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Grade 10 · Trigonometry

MEMORANDUM

Name:

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
Write down the value of sin30° without using a calculator.
(2)
12✓✓ (2)
2
Evaluate sin30° + cos60° without using a calculator.
(2)
12 + 12 = 1✓✓ (2)
3
Evaluate tan60° × cos30° without using a calculator.
(2)
3 × 32 = 32✓✓ (2)
4
Write down the value of cosec30°.
(2)
1sin30° = 112 = 2✓✓ (2)
5
Write down sec60°.
(2)
1cos60° = 2✓✓ (2)
6
Write down cot45°.
(2)
1tan45° = 1✓✓ (2)
7
Solve for θ if 2 sinθ = 1 and θ ∈ [0° ; 90°].
(2)
sinθ = 12 → θ = 30°✓✓ (2)
8
Solve for θ if 3 tanθ − 3 = 0 and θ ∈ [0° ; 90°].
(2)
tanθ = 1 → θ = 45°✓✓ (2)
9
Solve for θ if cos2θ = 0,5 and θ ∈ [0° ; 90°].
(2)
2θ = 60° → θ = 30°✓✓ (2)
10
Why is tan90° undefined?
(2)
tanθ = sinθcosθ and cos90° = 0, so it would mean dividing by zero.✓✓ (2)

TOTAL: 20 marks