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

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Grade 10 · Trigonometry

MEMORANDUM

Name:

Class:

Date:

Mark

/ 18

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 sin 30° without using a calculator.
(1)
1/2✓ (1)
2
Evaluate sin 30° + cos 60° without using a calculator.
(2)
1/2 + 1/2 = 1✓✓ (2)
3
Evaluate tan 60° × cos 30° without using a calculator.
(2)
√3 × (√3)/2 = 3/2✓✓ (2)
4
Write down the value of cosec30°.
(1)
1/(sin 30°) = 1/(1/2) = 2✓ (1)
5
Write down sec60°.
(1)
1/(cos 60°) = 2✓ (1)
6
Write down cot45°.
(1)
1/(tan 45°) = 1✓ (1)
7
Solve for θ if 2 sinθ = 1 and θ ∈ [0° ; 90°].
(2)
sinθ = 1/2 → θ = 30°✓✓ (2)
8
Solve for θ if 3 tanθ − 3 = 0 and θ ∈ [0° ; 90°].
(3)
tanθ = 1 → θ = 45°✓✓✓ (3)
9
Solve for θ if cos 2θ = 0,5 and θ ∈ [0° ; 90°].
(3)
2θ = 60° → θ = 30°✓✓✓ (3)
10
Why is tan 90° undefined?
(2)
tanθ = sinθ/cosθ and cos 90° = 0, so it would mean dividing by zero.✓✓ (2)

TOTAL: 18 marks