Inverse Trig Quizzes, Questions & Answers

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Inverse Sine Quizzes

Ready to turn sine equations into angles? This quiz helps you use arcsin to solve equations of the form sin(x) = k, identify principal values, and interpret additional solutions wh...

Questions: 20 | Attempts: 20 | Last updated: Dec 11, 2025

Sample Question
Solve for x (principal value): sin(x) = 1/2.

π/3

π/4

π/6

−π/6

Inverse Sine: Evaluate & Interpret (Principal Values)

Get comfortable with arcsin by learning how to interpret, evaluate, and connect inverse sine to the unit circle. In this quiz, you’ll find exact values like π/6, π/4, a...

Questions: 20 | Attempts: 11 | Last updated: Dec 11, 2025

Sample Question
Evaluate arcsin(1/2) in radians.

π/6

π/3

π/4

π/2

Real-World Modeling with Inverse Sine

Apply arcsin to realistic situations — from ramps, ladders, and waves to motion and design problems. You’ll model physical relationships like θ = arcsin(opposite ...

Questions: 20 | Attempts: 11 | Last updated: Dec 11, 2025

Sample Question
A cable exerts tension T = 800 N at angle θ, producing a vertical component Tᵥ = 400 N. Find θ in degrees.

22.5°

30°

45°

60°

All Inverse Sine Quizzes

Inverse Cosine Quizzes

the dreaded trig quiz

This trigonometry quiz tests knowledge on cosine ratios, triangle side calculations, angle determinations, inverse functions, and Pythagoras' theorem.

Questions: 10 | Attempts: 146 | Last updated: Mar 19, 2025

Sample Question
What is the ratio for Cosine?

Opposite/hypotenuse

Adjacent/hypotenuse

Hypotenuse/opposite

Hypotenuse/adjacent

Trigonometry and Angles Quiz: Do You Know When to Use the Inverse?

This quiz assesses your understanding of inverse trigonometric functions within the context of right triangle trigonometry. It presents a series of 40 problems requiring the applic...

Questions: 40 | Attempts: 115 | Last updated: Oct 03, 2025

Sample Question
The triangle below can be solved using trigonometry. Will it require an inverse ratio?

Yes

No

Solving Equations with Inverse Cosine

Now it’s time to put inverse cosine to work in equation solving. Here, you’ll solve trigonometric equations step by step, finding all solutions for θθ&...

Questions: 20 | Attempts: 10 | Last updated: Dec 03, 2025

Sample Question
Solve for θ in [0, 2π]: cos(θ) = −√2/2

3π/4 , 5π/4

π/4 , 7π/4

π/3 , 5π/3

2π/3 , 4π/3

All Inverse Cosine Quizzes

Inverse Tangent Quizzes

x010 Trigonometry Find Angle from 3 Sides

When asked for a fraction, do not simplify ie if the answer is 2/4 do not simplify to 1/2

Questions: 30 | Attempts: 65 | Last updated: Apr 21, 2025

Sample Question
The triangle below gives the lengths of all three sides, and asks to find the angle. If this problem is to be solved using a tan ratio, what fraction will be created for the inverse tan calculation?

72/54

Real-World Modeling with Inverse Tangent

Connect mathematics to real-life scenarios involving slopes, elevations, and viewing angles. In this quiz, you will apply an inverse tangent to determine angles of elevation, depre...

Questions: 20 | Attempts: 13 | Last updated: Dec 11, 2025

Sample Question
A ship is 500 m from a 100 m cliff. Find the angle of elevation to the top of the cliff (nearest tenth).

9.5°

10.8°

11.3°

12.0°

Inverse Tangent Quiz: Inverse Tangent Fundamentals

What sets inverse tangent apart from other inverse trig functions? In this quiz, you’ll explore arctangent’s restricted range, analyze how it maps slopes to angles, and...

Questions: 20 | Attempts: 10 | Last updated: Dec 17, 2025

Sample Question
Which of the following are true about the inverse tangent function?

Arctan(1) = π/4

Arctan(−√3/2) = −π/3

Arctan(x) has a period of 2π

Arctan(x) maps negative x to negative values

All Inverse Tangent Quizzes

Graphs Of Inverses Quizzes

Identifying Graphs of Inverse Cosine

Ready to explore the world of inverse trig graphs? In this quiz, you’ll dive into the shape, domain, and range of y = arccos(x) and learn how it connects to the cosine f...

Questions: 20 | Attempts: 10 | Last updated: Dec 10, 2025

Sample Question
Which pair gives the domain and range of y = arccos(x)?

Domain (−∞, ∞), range (−∞, ∞)

Domain [−1, 1], range [0, π]

Domain [0, π], range [−1, 1]

Domain [−π, π], range [−1, 1]

Identifying Graphs of Inverse Tangent

Ready to tackle the graph of y = arctan(x)? This quiz will help you visualize how the inverse tangent curve behaves — increasing smoothly with horizontal asymptotes and passi...

Questions: 20 | Attempts: 10 | Last updated: Dec 10, 2025

Sample Question
Which pair gives the domain and range of y = arctan(x)?

(−∞, ∞), Range (−π/2, π/2)

[−1, 1], Range [0, π]

[0, π], Range [−1, 1]

[−π, π], Range [−1, 1]

Transformations of Inverse Trig Graphs

Want to master how inverse trig graphs shift, flip, and move? In this quiz, you’ll explore how vertical and horizontal shifts, reflections, and transformations affect the gra...

Questions: 20 | Attempts: 10 | Last updated: Dec 10, 2025

Sample Question
The graph of y = arcsin(x) + π/4 is obtained from y = arcsin(x) by which transformation?

Reflection over the x-axis

Horizontal shift left by π/4

Vertical shift upward by π/4

Vertical shift downward by π/4

All Graphs Of Inverses Quizzes

Principal Values Quizzes

Principal Values: Defining Inverse Trig & Restricted Domains

Ready to learn how inverse trigonometric functions are defined by carefully restricting domains to make them valid functions? This quiz focuses on identifying corre...

Questions: 20 | Attempts: 15 | Last updated: Dec 11, 2025

Sample Question
Which function has an inverse only if its domain is restricted to [−π/2, π/2]?

Sin(x)

Tan(x)

Cos(x)

Csc(x)

Solve Equations & Model with Principal Values

Ready to apply principal values to real-life and modeling scenarios? This quiz connects inverse trigonometric equations to geometric contexts like ladders, ramps, hills, and s...

Questions: 20 | Attempts: 12 | Last updated: Dec 11, 2025

Sample Question
Solve sin(x) = 1/2 for the principal value.

X = π/6

X = 5π/6

X = −π/6

X = π/2

Principal Value Quiz: Principal Value and Restricted Domains

Why do trigonometric inverses rely on principal values? In this quiz, you’ll explore the idea of restricting domains so that each inverse function yields a single, meaningful...

Questions: 20 | Attempts: 10 | Last updated: Dec 17, 2025

Sample Question
Which restriction makes sin x one-to-one and symmetric about the origin?

[−π/2, π/2]

[0, π]

(−π, 0]

[π/2, 3π/2]

All Principal Values Quizzes

Real World Use Quizzes

Special Triangles in Real Life

Ready to see how special triangles appear all around you? In this quiz, you’ll use triangles to solve everyday geometry problems. You’ll calculate heights, distanc...

Questions: 20 | Attempts: 10 | Last updated: Dec 10, 2025

Sample Question
A ladder leans against a wall forming an angle of π/6 with the ground. If the ladder is 12 m long, how high up the wall does it reach?

6 m

4√3 m

12√3 m

2√3 m

Inverse Trig in Real Life

Curious how to find angles when you already know the sides? In this quiz, you’ll use inverse trigonometric functions — arcsin, arccos, and arctan — to solve ...

Questions: 20 | Attempts: 10 | Last updated: Dec 10, 2025

Sample Question
A right triangle has opposite side 3 and adjacent side 4. What is the acute angle?

Arcsin(4/5)

Arctan(4/3)

Arctan(3/4)

Arccos(3/5)

All Real World Use Quizzes

Top Trending Inverse Trig Quizzes

Plane And Spherical Trigonometry Quiz

Click on the option that corresponds to the CORRECT answer.

Questions: 20 | Attempts: 292 | Last updated: Aug 22, 2025

Sample Question 1
What is the value of Arcsin 0?

0

Sample Question 2
What is the value of Arccos(-1)

0

Inverse Trig Quizzes, Questions & Answers

Popular Inverse Trig Topics

Inverse Sine Quizzes

Inverse Cosine Quizzes

Inverse Tangent Quizzes

Graphs Of Inverses Quizzes

Principal Values Quizzes

Real World Use Quizzes

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