Advanced Trigonometric Analysis

Trigonometry

A collection of high-school level trigonometric problems focusing on identities, unit circle properties, and inverse functions.

mathematics geometry calculus-prep

12 Questions Hard Ages 15+ Aug 1, 2026

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About this Study Set

This study set covers Trigonometry through 12 practice questions. A collection of high-school level trigonometric problems focusing on identities, unit circle properties, and inverse functions. Every question includes the correct answer so you can learn as you go — pick any format above to get started.

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Browse all 12 questions from the Advanced Trigonometric Analysis study set below. Each question shows the correct answer — select a study format above to practice interactively.

1 What is the exact value of cos(7π/12)?

A (√2 - √6)/4
B (√6 - √2)/4
C (-√6 - √2)/4
D (√2 + √6)/4

2 Given sin(θ) = 3/5 and θ is in the second quadrant, what is the exact value of tan(2θ)?

A -24/7
B 24/7
C 7/24
D -7/24

3 What is the period of the function f(x) = 3tan(2x - π/4)?

A π/4
B π/2
C π
D 2π

4 Which expression is equivalent to (1 - cos(2θ)) / sin(2θ)?

A sin(θ)
B cos(θ)
C tan(θ)
D cot(θ)

5 What is the range of the function f(x) = 4arcsin(x/2) - π?

A [-3π/2, π/2]
B [-π, π]
C [-2π, 2π]
D [-5π/2, π/2]

6 For the equation cos²(θ) + sin(θ) = 1, what is the sum of all solutions in the interval [0, 2π]?

A π
B 2π
C 3π
D 4π

7 If sec(θ) = -5/3 and π < θ < 3π/2, what is the value of sin(θ)?

A 4/5
B -4/5
C 3/5
D -3/5

8 What is the exact value of sin(arctan(1/2) + arctan(1/3))?

A 1/√2
B 1
C 1/2
D √3/2

9 What is the general solution for sin(x) = cos(x)?

A nπ + π/4
B nπ - π/4
C 2nπ + π/4
D nπ + π/2

10 Which of the following is equivalent to cos(A + B)cos(A - B)?

A cos²A - sin²B
B cos²A + sin²B
C sin²A - cos²B
D sin²A + cos²B

11 If f(x) = 2sin(x)cos(x), what is the derivative f'(x) at x = π/6?

A -1
B 0
C 1/2
D 1

12 What is the value of arccos(cos(5π/4))?

A 5π/4
B 3π/4
C π/4
D -π/4

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