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Trigonometric Identities MCQs — Mathematics (page 2)

42 multiple-choice questions on Trigonometric Identities from Mathematics, each with the correct answer and, where available, a teacher's explanation. Read through them to revise the chapter, then practise the same questions one by one to test yourself.

26. If costheta = 1517 and theta is acute, find csctheta.

  1. 1517
  2. 178
  3. 817
  4. 815

Answer: B) 178

Explanation: Draw a right triangle with opposite = 8, adjacent = 15, hypotenuse = 17 (Pythagoras: 8^2 + 15^2 = 17^2). Then csctheta = 178. SLO M-09-B-24 · Application

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27. If tantheta = 512 and theta is acute, find sectheta.

  1. 1213
  2. 513
  3. 512
  4. 1312

Answer: D) 1312

Explanation: Draw a right triangle with opposite = 5, adjacent = 12, hypotenuse = 13 (Pythagoras: 5^2 + 12^2 = 13^2). Then sectheta = 1312. SLO M-09-B-24 · Application

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28. Which expression is identical to cos^2theta(1 + tan^2theta)?

  1. sin^2theta
  2. 1
  3. sec^2theta
  4. cos^2theta

Answer: B) 1

Explanation: Using sin^2theta + cos^2theta = 1 and the definitions of the ratios, cos^2theta(1 + tan^2theta) = 1. SLO M-09-B-23 · Knowledge

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29. If sintheta = 817 and theta is acute, find cottheta.

  1. 158
  2. 815
  3. 817
  4. 1517

Answer: A) 158

Explanation: Draw a right triangle with opposite = 8, adjacent = 15, hypotenuse = 17 (Pythagoras: 8^2 + 15^2 = 17^2). Then cottheta = 158. SLO M-09-B-24 · Application

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30. If sintheta = 12 and theta is acute, then costheta =

  1. 1 3
  2. 3
  3. 12
  4. 32

Answer: D) 32

Explanation: costheta = 1 - 14 = 32. SLO M-09-B-24 · Application

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31. If costheta = 4041 and theta is acute, find tantheta.

  1. 941
  2. 940
  3. 4140
  4. 4041

Answer: B) 940

Explanation: Draw a right triangle with opposite = 9, adjacent = 40, hypotenuse = 41 (Pythagoras: 9^2 + 40^2 = 41^2). Then tantheta = 940. SLO M-09-B-24 · Application

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32. A ramp makes an angle theta with the ground, where sintheta = 513. For a ramp 26 m long, the horizontal distance it covers is:

  1. 20 m
  2. 26 m
  3. 10 m
  4. 24 m

Answer: D) 24 m

Explanation: costheta = 1 - 25169 = 1213; horizontal = 26 1213 = 24 m. SLO M-09-B-24 · Application

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33. If costheta = 35 and theta is acute, find sintheta.

  1. 53
  2. 45
  3. 35
  4. 43

Answer: B) 45

Explanation: Draw a right triangle with opposite = 4, adjacent = 3, hypotenuse = 5 (Pythagoras: 4^2 + 3^2 = 5^2). Then sintheta = 45. SLO M-09-B-24 · Application

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34. Which expression is identical to (sintheta + costheta)^2?

  1. 1 + 2sinthetacostheta
  2. 1 - 2sinthetacostheta
  3. 1
  4. 2

Answer: A) 1 + 2sinthetacostheta

Explanation: Using sin^2theta + cos^2theta = 1 and the definitions of the ratios, (sintheta + costheta)^2 = 1 + 2sinthetacostheta. SLO M-09-B-23 · Knowledge

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35. Which expression is identical to sec^2theta - tan^2theta?

  1. 1
  2. sectheta
  3. 2sec^2theta
  4. 0

Answer: A) 1

Explanation: Using sin^2theta + cos^2theta = 1 and the definitions of the ratios, sec^2theta - tan^2theta = 1. SLO M-09-B-23 · Knowledge

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36. Which expression is identical to sin^2theta + cos^2theta?

  1. tan^2theta
  2. 2
  3. 1
  4. 0

Answer: C) 1

Explanation: Using sin^2theta + cos^2theta = 1 and the definitions of the ratios, sin^2theta + cos^2theta = 1. SLO M-09-B-23 · Knowledge

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37. Which expression is identical to sintheta1 - costheta?

  1. sintheta1 + costheta
  2. 1 - costhetasintheta
  3. tantheta
  4. 1 + costhetasintheta

Answer: D) 1 + costhetasintheta

Explanation: Using sin^2theta + cos^2theta = 1 and the definitions of the ratios, sintheta1 - costheta = 1 + costhetasintheta. SLO M-09-B-23 · Knowledge

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38. A ladder makes angle theta with the ground where costheta = 35. If the ladder is 10 m long, how high up the wall does it reach?

  1. 10 m
  2. 6 m
  3. 8 m
  4. 4 m

Answer: C) 8 m

Explanation: sintheta = 45; height = 10 45 = 8 m. SLO M-09-B-24 · Application

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39. If tantheta = 1, the value of sec^2theta is:

  1. 0
  2. 2
  3. 1
  4. 2

Answer: D) 2

Explanation: sec^2theta = 1 + tan^2theta = 2. SLO M-09-B-24 · Application

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40. If sintheta = 35 and theta is acute, find costheta.

  1. 54
  2. 35
  3. 45
  4. 34

Answer: C) 45

Explanation: Draw a right triangle with opposite = 3, adjacent = 4, hypotenuse = 5 (Pythagoras: 3^2 + 4^2 = 5^2). Then costheta = 45. SLO M-09-B-24 · Application

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41. If tantheta = 1235 and theta is acute, find sintheta.

  1. 3537
  2. 1235
  3. 1237
  4. 3735

Answer: C) 1237

Explanation: Draw a right triangle with opposite = 12, adjacent = 35, hypotenuse = 37 (Pythagoras: 12^2 + 35^2 = 37^2). Then sintheta = 1237. SLO M-09-B-24 · Application

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42. Which expression is identical to costhetacsctheta?

  1. cottheta
  2. tantheta
  3. sectheta
  4. 1

Answer: A) cottheta

Explanation: Using sin^2theta + cos^2theta = 1 and the definitions of the ratios, costhetacsctheta = cottheta. SLO M-09-B-23 · Knowledge

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