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AP Intermediate 1st Year Trigonometric Functions — practice questions — page 2

Explore 50 free Trigonometric Functions questions in AP Intermediate 1st Year 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 31–50 of 50.

The identity $\sin 2A$ equals:Read the answer and worked solution →The fundamental Pythagorean identity in trigonometry is:Read the answer and worked solution →The general solution of sin θ = 1/2 is:Read the answer and worked solution →The principal value range of sin⁻¹(x) is:Read the answer and worked solution →In a triangle ABC, the Law of Sines states:Read the answer and worked solution →Match each trigonometric identity to its equivalent.Read 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

The identity $\sin 2A$ equals:

  1. $2\sin A\cos A$, the standard double-angle formula on the chart
  2. $\sin^2 A + \cos^2 A$, equal to $1$ by Pythagorean identity
  3. $2\sin^2 A$, missing the cosine factor in the formula
  4. $\sin A + \cos A$, the simple sum of the trig functions
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Correct answer: A. $2\sin A\cos A$, the standard double-angle formula on the chart

Double-angle: $\sin 2A = 2\sin A\cos A$.

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The fundamental Pythagorean identity in trigonometry is:

  1. $\sin^2\theta + \cos^2\theta = 1$
  2. $\tan^2\theta + \cot^2\theta = 1$
  3. $\sin\theta + \cos\theta = 1$
  4. $\sin\theta \cos\theta = 1$
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Correct answer: A. $\sin^2\theta + \cos^2\theta = 1$

**The fundamental Pythagorean identity:** sin²θ + cos²θ = 1 (from x² + y² = 1 on unit circle). **Other forms:** 1 + tan²θ = sec²θ; 1 + cot²θ = cosec²θ.

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The general solution of sin θ = 1/2 is:

  1. $\theta = \pi/6$ only (principal value)
  2. $\theta = n\pi/6$ for any n
  3. $\theta = 2n\pi + \pi/6$ only
  4. $\theta = n\pi + (-1)^n \pi/6$, n ∈ ℤ
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Correct answer: D. $\theta = n\pi + (-1)^n \pi/6$, n ∈ ℤ

General solution for sin θ = sin α: θ = nπ + (-1)^n α, n ∈ ℤ. Here α = π/6, so θ = nπ + (-1)^n (π/6). At n=0: π/6 ✓. At n=1: π − π/6 = 5π/6 ✓.

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