About this Study Set
This study set covers Mathematics through
25 practice questions.
A comprehensive assessment of high-level trigonometric identities, properties, and analytical functions. Every question includes the correct answer so you can learn as you go — pick any format above to get started.
Questions & Answers
Browse all 25 questions from the
Advanced High School Trigonometry study set below.
Each question shows the correct answer — select a study format above to practice interactively.
1
What is the exact value of sin(15°) using the angle subtraction formula?
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A
(√6 - √2)/4
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B
(√6 + √2)/4
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C
(√3 - 1)/2
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D
(√2 - √3)/4
2
For the function f(x) = 3cos(2x - π) + 1, what is the correct period?
3
Which expression is equivalent to (1 - cos(2θ)) / sin(2θ)?
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A
tan(θ)
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B
cot(θ)
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C
sin(θ)
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D
sec(θ)
4
What is the domain of the function f(x) = sec(x)?
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A
x ≠ nπ, n ∈ Z
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B
x ≠ (2n+1)π/2, n ∈ Z
-
C
x ≠ 2nπ, n ∈ Z
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D
All real numbers
5
If tan(θ) = 3/4 and θ is in the third quadrant, what is the value of cos(θ)?
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A
4/5
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B
3/5
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C
-4/5
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D
-3/5
6
Which identity represents the double-angle formula for cos(2θ) in terms of sin only?
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A
1 - 2sin²(θ)
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B
2sin²(θ) - 1
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C
1 + 2sin²(θ)
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D
cos²(θ) - sin²(θ)
7
What is the general solution for the equation sin(x) = 1/2?
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A
x = nπ + (-1)^n(π/6)
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B
x = 2nπ ± π/6
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C
x = nπ + π/6
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D
x = nπ - π/6
8
The range of the inverse function f(x) = arccos(x) is defined as:
-
A
(-π/2, π/2)
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B
[0, π]
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C
[-π/2, π/2]
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D
(0, π)
9
Using the harmonic addition theorem, express √3sin(x) + cos(x) in the form Rsin(x + α).
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A
2sin(x + π/6)
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B
2sin(x + π/3)
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C
√3sin(x + π/6)
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D
2sin(x - π/6)
10
What is the derivative of f(x) = tan(x)?
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A
sec(x)
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B
sec²(x)
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C
csc²(x)
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D
-sec²(x)
11
For a triangle with sides a, b, c and angle C opposite to side c, what is the Cosine Rule?
-
A
c² = a² + b² - 2ab cos(C)
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B
c² = a² + b² + 2ab cos(C)
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C
a² = b² + c² - 2bc cos(A)
-
D
c² = a² + b² - ab cos(C)
12
Which value is equal to sin(75°)cos(15°) + cos(75°)sin(15°)?
13
What is the period of the function y = tan(bx)?
14
If sec²(θ) - tan²(θ) = k, what is the value of k?
-
A
0
-
B
1
-
C
sec(θ)
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D
tan(θ)
15
The value of sin(arccos(x)) for |x| ≤ 1 is:
-
A
√(1 - x²)
-
B
1 - x²
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C
x
-
D
1/√(1 - x²)
16
Which of the following is an odd function?
-
A
f(x) = cos(x)
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B
f(x) = sec(x)
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C
f(x) = sin(x)
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D
f(x) = |sin(x)|
17
If 0 ≤ θ < 2π, how many solutions exist for sin(2θ) = 1/2?
18
The identity cos(A + B) + cos(A - B) is equal to:
-
A
2cos(A)cos(B)
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B
2sin(A)sin(B)
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C
2cos(A)sin(B)
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D
2sin(A)cos(B)
19
What is the limit of sin(x)/x as x approaches 0?
20
If cot(θ) = -√3 and π/2 < θ < π, what is the value of θ?
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A
2π/3
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B
5π/6
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C
7π/6
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D
11π/6
21
Which expression is equivalent to csc²(θ) - 1?
-
A
sec²(θ)
-
B
tan²(θ)
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C
cot²(θ)
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D
sin²(θ)
22
What is the exact value of cos(11π/12)?
-
A
-(√6 + √2)/4
-
B
(√6 - √2)/4
-
C
-(√6 - √2)/4
-
D
(√6 + √2)/4
23
The function y = sin(x) is increasing on which interval within [0, 2π]?
-
A
(0, π)
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B
(0, π/2) and (3π/2, 2π)
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C
(π/2, 3π/2)
-
D
(0, 2π)
24
Simplify sin(θ + 3π/2).
-
A
cos(θ)
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B
-cos(θ)
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C
sin(θ)
-
D
-sin(θ)
25
What is the amplitude of the function y = -4sin(x) + 2?
