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WBJEE Trigonometric Functions — practice questions — page 2

Explore 54 free Trigonometric Functions questions in WBJEE 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 31–54 of 54.

If sin θ = 12/13 (acute θ in Q1), find tan(θ/2):Read the answer and worked solution →Minimum value of sin²θ + cos⁴θ:Read the answer and worked solution →If sin θ = 12/13 (acute), find tan(θ/2):Read the answer and worked solution →In triangle with sides 7, 8, 9, find cos of the angle opposite to side 9 (use cosine rule):Read the answer and worked solution →General solution of sin θ = sin α:Read the answer and worked solution →SAT · Mathematics · Trig Ratios (SOHCAHTOA)Read the answer and worked solution →SAT · Mathematics · Trig Identities — T/FRead the answer and worked solution →Match the trig identity to its resultRead the answer and worked solution →Match the trig valueRead the answer and worked solution →Fill the gaps in the triangle area ruleRead the answer and worked solution →Positive or negative angleRead the answer and worked solution →Which ratios are positiveRead the answer and worked solution →Type the trig functionRead the answer and worked solution →Pop what is defined everywhereRead the answer and worked solution →Which unit of angleRead the answer and worked solution →One word is wrongRead the answer and worked solution →Order the build upRead the answer and worked solution →Sine and cosineRead the answer and worked solution →Which one does not belongRead the answer and worked solution →Which way does it turnRead the answer and worked solution →Spot the false statementRead the answer and worked solution →Which ones belongRead the answer and worked solution →Knock out the true statementsRead the answer and worked solution →Trigonometry bingoRead the answer and worked solution →

Worked practice questions

If sin θ = 12/13 (acute θ in Q1), find tan(θ/2):

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

cos θ = √(1 − sin²θ) = √(1 − 144/169) = √(25/169) = 5/13 (positive in Q1). We have tan(θ/2) = (1 − cos θ)/sin θ. That is tan(θ/2) = (1 − 5/13)/(12/13). That is tan(θ/2) = (8/13)/(12/13). That is tan(θ/2) = 8/12. So tan(θ/2) = 2/3.

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Minimum value of sin²θ + cos⁴θ:

  1. 1
  2. 3/4
  3. 1/2
  4. 1/4
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Correct answer: B. 3/4

Let x = sin²θ. Then cos²θ = 1 - x, cos⁴θ = (1-x)². Expression = x + (1-x)² = x + 1 - 2x + x² = x² - x + 1. Derivative: 2x - 1 = 0 → x = 1/2. Min value = 1/4 - 1/2 + 1 = 3/4.

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If sin θ = 12/13 (acute), find tan(θ/2):

  1. 5/12
  2. Cannot determine
  3. 1/5
  4. 2/3
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Correct answer: C. 1/5

For acute θ with sinθ = 12/13: cosθ = 5/13 (positive in Q1). tan(θ/2) = sinθ/(1 + cosθ) = (12/13)/(1 + 5/13) = (12/13)/(18/13) = 12/18 = 2/3. Hmm answer A is 1/5 my calc gives 2/3. Let me recheck. tan(θ/2) = (1 - cosθ)/sinθ = (1 - 5/13)/(12/13) = (8/13)/(12/13) = 8/12 = 2/3. So actually 2/3 is correct, which matches option C, not A. Setting answer to C.

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