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Quizzes > Mathematics

Interactive Trigonometry Quiz to Practice Angles and Triangles

Quick, free practice to test your skills with an online trigonometry test. Instant results.

Editorial: Review CompletedCreated By: Ria MalhotraUpdated Aug 27, 2025
Difficulty: Moderate
2-5mins
Learning OutcomesCheat Sheet
Paper art illustration for trigonometry quiz on golden yellow background

This trigonometry quiz helps you practice angles, side lengths, and real-world problems, check your understanding, and spot topics to review. Then build confidence with a unit circle quiz, a right triangle trigonometry quiz, or a trig identities quiz for targeted practice and faster recall.

What is the value of sin(30°)?
?2/2
?3/2
1/2
1/?3
The sine of 30° is defined as the y-coordinate of the corresponding point on the unit circle, which is 1/2. This is a fundamental value in trigonometry and appears in many right-triangle calculations. Memorizing these special angles helps solve more complex problems. .
What is the value of cos(60°)?
?3/2
1/2
0
?2/2
The cosine of 60° equals the x-coordinate on the unit circle at that angle, which is 1/2. This value is vital in solving right triangles and appears frequently in physics and engineering. Recognizing these key angles speeds up problem solving. .
What is the value of tan(45°)?
?3
0
?2
1
Tangent is sine divided by cosine. At 45°, both sine and cosine are equal (?2/2), so their ratio is 1. This is a key identity used in many trig problems. .
Convert 150° to radians.
?/3
3?/4
5?/6
2?/3
To convert degrees to radians, multiply by ?/180. So 150° × ?/180 = (150/180)? = 5?/6. Converting between degrees and radians is essential when working in calculus or physics. .
A surveyor stands 100 meters from the base of a building and measures the angle of elevation to the top as 30°. What is the building's height (to one decimal place)?
57.7 m
173.2 m
100.0 m
50.0 m
Height = distance × tan(angle). Here tan(30°) = 1/?3 ?0.577, so height ?100×0.577 = 57.7?m. This real-world application of tangent is common in surveying. .
What is the value of cos(120°)?
?3/2
-?3/2
1/2
-1/2
120° lies in the second quadrant where cosine is negative. Its reference angle is 60°, and cos(60°)=1/2, so cos(120°)=?1/2. Understanding quadrants helps determine sign of trig values. .
In triangle ABC, angle A = 50°, angle B = 60°, and side a (opposite A) = 7. Use the Law of Sines to find side b (opposite B).
?7.91
?5.50
?6.07
?8.50
Law of Sines: b/sin(B) = a/sin(A). So b = (sin(60°)×7)/sin(50°) ? (0.8660×7)/0.7660 ?7.91. This formula solves non-right triangles. .
What is the exact value of sin(75°)?
(?6 - ?2) / 4
(?3 + 1) / 2
(?6 + ?2) / 4
?2 / 2
Use the angle-addition formula: sin(75°)=sin(45°+30°)=sin45cos30+cos45sin30 = (?2/2)(?3/2)+(?2/2)(1/2) = (?6+?2)/4. This exact form is useful in exact-value problems. .
Solve 2 cos²(x) ? 1 = 0 for x in [0°, 360°).
30°, 150°, 210°, and 330°
45°, 135°, 225°, and 315°
60° and 300°
90° and 270°
2 cos²(x)?1=0 ? cos²(x)=1/2 ? cos(x)=±?2/2. Angles in [0°,360°) where cosine is ±?2/2 are 45°, 135°, 225°, and 315°. Recognizing unit-circle values is key. .
Solve sin(x) = -1/2 for x in [0, 2?).
5?/6 and 7?/6
?/6 and 5?/6
11?/6 and 13?/6
7?/6 and 11?/6
sin(x) = -1/2 occurs where the reference angle is ?/6 in the third and fourth quadrants. These correspond to x = 7?/6 and 11?/6 in [0,2?). Mastery of quadrants and reference angles is essential. .
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Study Outcomes

  1. Understand Fundamental Trigonometric Ratios -

    Identify the sine, cosine, and tangent relationships in right triangles and explain how they interrelate.

  2. Calculate Unknown Sides and Angles -

    Apply SOHCAHTOA and inverse trigonometric functions to determine missing measurements in right triangles.

  3. Solve Real-World Problems -

    Translate practical scenarios into trigonometric equations and compute solutions similar to those featured in an online trigonometry quiz.

  4. Analyze Triangle Configurations -

    Evaluate acute, obtuse, and right triangle cases to select the appropriate trigonometric methods for each scenario.

  5. Evaluate Your Trigonometry Quiz Performance -

    Review results from this trigonometry quiz part 1 to pinpoint strengths and target areas for improvement.

  6. Build Confidence for Your Trigonometry Test -

    Develop strategies to improve speed and accuracy in preparation for your next trigonometry test.

Cheat Sheet

  1. Fundamental Trigonometric Ratios -

    Review sine, cosine, and tangent definitions in a right triangle using the SOHCAHTOA mnemonic (Source: Khan Academy). For example, sin(θ)=opposite/hypotenuse, cos(θ)=adjacent/hypotenuse, and tan(θ)=opposite/adjacent. Mastering these basics will boost your confidence on any trigonometry test.

  2. Unit Circle and Radian Measure -

    Understand how angles correspond to coordinates on the unit circle and convert between degrees and radians (Source: MIT OpenCourseWare). Remember that key angles (0, π/6, π/4, π/3, π/2) map to familiar (x,y) pairs like (√3/2, 1/2). This is invaluable when you face trig questions in an online trigonometry quiz.

  3. Pythagorean Identities -

    Memorize identities such as sin²θ + cos²θ = 1 and 1 + tan²θ = sec²θ (Source: Wolfram MathWorld). Practice deriving related forms like cos²θ = 1 - sin²θ for quick algebraic simplifies. These are frequently tested in trigonometry quiz part 1 and real-world problem sets.

  4. Law of Sines and Cosines -

    Learn to solve non-right triangles using a/sin A = b/sin B = c/sin C and c² = a² + b² - 2ab cos C (Source: Purplemath). Apply them to find missing sides or angles in oblique triangles encountered in surveyor or navigation problems. These formulas appear often in advanced trigonometry test sections.

  5. Inverse Trigonometric Functions -

    Practice using arcsin, arccos, and arctan to solve for angles when given a ratio (Source: University of Texas at Austin). For instance, θ = arctan(opposite/adjacent) lets you back-solve right-triangle angles. Mastery of inverses is key for higher-level questions on any trig quiz.

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