Trigonometry

JKSSB Junior Engineer (Mechanical) · Mathematics · 96 practice questions with answers and explanations: 47 Easy, 49 Medium, 0 Hard.

Sample questions

Sample Easy question 1

If x = r cosθ and y = r sinθ, eliminate θ to find a relation between x, y and r.

  1. x² + y² = r²
  2. xy = r²
  3. x + y = r
  4. x² - y² = r²
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Answer: A. x²+y² = r²cos²θ + r²sin²θ = r²(sin²θ+cos²θ) = r².

Sample Easy question 2

If sec A = 2 (A acute), find the value of A.

  1. 30°
  2. 90°
  3. 45°
  4. 60°
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Answer: D. sec A = 2 means cos A = 0.5, so A = 60°.

Sample Easy question 3

If cosec A = 2 (A acute), find the value of A.

  1. 30°
  2. 45°
  3. 60°
  4. 90°
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Answer: A. cosec A = 2 means sin A = 0.5, so A = 30°.

Sample Medium question 4

If tan A = 3/4 and A is acute, find sin A + cos A.

  1. 1.2
  2. 1.6
  3. 1.4
  4. 1.8
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Answer: C. With the 3-4-5 triangle, sin A = 3/5, cos A = 4/5; sum = 7/5 = 1.4.

Sample Medium question 5

If tan A = 5/12 and A is acute, find sin A + cos A.

  1. 1.36
  2. 1.46
  3. 1.41
  4. 1.31
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Answer: D. With the 5-12-13 triangle, sin A = 5/13, cos A = 12/13; sum = 17/13 ≈ 1.31.

Sample Medium question 6

If tan A = 8/15 and A is acute, find sin A - cos A.

  1. -0.31
  2. -0.45
  3. -0.35
  4. -0.41
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Answer: D. With the 8-15-17 triangle, sin A = 8/17, cos A = 15/17; difference = -7/17 ≈ -0.41.

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