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Indian Navy MR Trigonometric Functions — practice questions

Explore 4 free Trigonometric Functions questions in Indian Navy MR Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Trigonometric Functions questions and exercises with answers

Showing questions 1–4 of 4.

$\sin(180° - \theta)$ equals:Read the answer and worked solution →sin(A + B) equals:Read the answer and worked solution →If tan θ = 1/2 (acute), find sin 2θ:Read the answer and worked solution →If sin θ = 12/13 (acute θ in Q1), find tan(θ/2):Read the answer and worked solution →

Worked practice questions

$\sin(180° - \theta)$ equals:

  1. $-\cos\theta$
  2. $-\sin\theta$
  3. $\sin\theta$
  4. $\cos\theta$
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Correct answer: C. $\sin\theta$

Supplementary-angle identity: $\sin(180° - \theta) = \sin\theta$. Reason: sine is positive in the second quadrant (where $180° - \theta$ lies for $0° < \theta < 180°$), and the reference angle is $\theta$. Companion identities: - $\cos(180° - \theta) = -\cos\theta$ - $\tan(180° - \theta) = -\tan\theta$

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sin(A + B) equals:

  1. cosA cosB - sinA sinB
  2. sinA cosB - cosA sinB
  3. sinA cosB + cosA sinB
  4. sinA + sinB
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Correct answer: C. sinA cosB + cosA sinB

**Compound angle formula:** sin(A + B) = sinA cosB + cosA sinB. (And sin(A - B) = sinA cosB - cosA sinB.)

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If tan θ = 1/2 (acute), find sin 2θ:

  1. 1/5
  2. 3/5
  3. 4/5
  4. 2/5
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Correct answer: C. 4/5

sin 2θ = 2 sinθ cosθ. From tan = 1/2, draw right triangle: opp=1, adj=2, hyp=√5. sinθ = 1/√5, cosθ = 2/√5. So sin 2θ = 2(1/√5)(2/√5) = 4/5.

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