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Quizzes > Mathematics > Geometry

Master Trigonometric Ratios of Special Angles - Take the Quiz!

Put your skills to the test in our special angles trigonometry quiz!

Editorial: Review CompletedCreated By: Jezza Mae VenturaUpdated Aug 28, 2025
Difficulty: Moderate
2-5mins
Learning OutcomesCheat Sheet
Paper cut art of trig ratios including sine, cosine, tangent, protractor on golden yellow background.

This quiz helps you practice trigonometric ratios at special angles - 30°, 45°, and 60° - with sine, cosine, and tangent. Get instant feedback and clear explanations so you can spot gaps before a test while you work through each question at your own pace.

What is sin 30 degrees?
0
1/2 (since the 30-60-90 triangle has opposite/hypotenuse = 1/2)
sqrt(2)/2
sqrt(3)/2
undefined
Evaluate cos 60 degrees.
sqrt(2)/2
sqrt(3)/2
0
1/2 (adjacent/hypotenuse in a 30-60-90 triangle)
undefined
Find tan 45 degrees.
1 (legs equal in a 45-45-90 triangle)
0
sqrt(3)
1/sqrt(3)
undefined
Compute sin 90 degrees.
-1
0
undefined
1 (point is at (0,1) on the unit circle)
undefined
Determine cos 0 degrees.
1 (unit circle point is (1,0))
0
undefined
-1
undefined
Evaluate sin(π/6).
1/2 (π/6 is 30 degrees)
0
sqrt(3)/2
sqrt(2)/2
undefined
Evaluate cos(π/3).
-1/2
sqrt(3)/2
1/2 (π/3 is 60 degrees)
0
undefined
sin 150 degrees equals what exact value?
1/2 (reference angle 30 degrees; sine positive in QII)
-1/2
sqrt(3)/2
-sqrt(3)/2
undefined
cos 120 degrees is equal to which exact value?
-sqrt(3)/2
-1/2 (reference 60 degrees; cosine negative in QII)
1/2
sqrt(3)/2
undefined
tan 135 degrees equals what?
sqrt(3)
-1 (reference 45 degrees; tangent negative in QII)
1
-sqrt(3)
undefined
sin 210 degrees equals what?
-1/2 (reference 30 degrees; sine negative in QIII)
-sqrt(3)/2
1/2
sqrt(3)/2
undefined
cos 300 degrees equals what?
-sqrt(3)/2
1/2 (reference 60 degrees; cosine positive in QIV)
-1/2
sqrt(3)/2
undefined
tan 330 degrees equals what exact value?
sqrt(3)
-1/sqrt(3) (reference 30 degrees; tangent negative in QIV)
-sqrt(3)
1/sqrt(3)
undefined
Compute sin(3π/4).
1/2
-sqrt(2)/2
sqrt(2)/2 (reference π/4; sine positive in QII)
sqrt(3)/2
undefined
Compute cos(5π/6).
-1/2
sqrt(3)/2
-sqrt(3)/2 (reference π/6; cosine negative in QII)
1/2
undefined
Compute tan(7π/6).
1/sqrt(3) (reference π/6; tangent positive in QIII)
-1/sqrt(3)
-sqrt(3)
sqrt(3)
undefined
What is tan(2π/3)?
1/sqrt(3)
-1/sqrt(3)
-sqrt(3) (reference π/3; tangent negative in QII)
sqrt(3)
undefined
cos 240 degrees equals -1/2.
False
True
undefined
tan 150 degrees equals -1/sqrt(3).
False
True
undefined
If cos θ = sqrt(2)/2 and 90° < θ < 180°, what is sin θ?
-sqrt(2)/2
-sqrt(3)/2
sqrt(3)/2
sqrt(2)/2 (positive in QII with reference 45°)
undefined
0

Study Outcomes

  1. Identify Special Angle Ratios -

    Recall the exact sine, cosine, and tangent values for 30°, 45°, and 60° with confidence during trigonometric ratios practice.

  2. Apply Ratios to Triangle Problems -

    Use special angle sine, cosine, and tangent values to calculate missing side lengths in right triangles accurately.

  3. Compare Ratio Patterns -

    Analyze how trigonometric ratios change across 30°, 45°, and 60° to recognize underlying fraction and square root patterns.

  4. Interpret Quiz Results -

    Evaluate your performance on the special angles trigonometry quiz to identify strengths and areas for further study.

  5. Memorize Key Values -

    Commit crucial fraction and √-based values to memory for quick recall during math tests or problem-solving sessions.

  6. Boost Trigonometry Confidence -

    Strengthen your understanding of special angles and feel prepared to tackle more advanced trigonometric ratios questions.

Cheat Sheet

  1. Unit Circle Coordinates for 30°, 45°, and 60° -

    Memorize the exact (x,y) pairs on the unit circle - (√3/2, 1/2) at 30°, (√2/2, √2/2) at 45°, and (1/2, √3/2) at 60° - so you can instantly read off cosine (x) and sine (y). These values form the backbone of any special angles trigonometry quiz and are endorsed by academic sources like MIT OpenCourseWare. Practicing these coordinates in a quiz trigonometric ratios setting builds speed and confidence.

  2. 30° - 60° - 90° Triangle Ratios -

    Use the 30° - 60° - 90° right triangle where sides are in the ratio 1:√3:2 (short leg:long leg:hypotenuse) to derive sin 30°=1/2, cos 30°=√3/2, and tan 30°=1/√3. This concrete construction, found in university geometry texts, ensures you grasp why special angle sine, cosine, and tangent take those exact values. Sketching and labeling this triangle before a special angle sine cosine tangent drill is a proven study habit.

  3. 45° - 45° - 90° Triangle Ratios -

    Recall that in a 45° - 45° - 90° triangle, the legs are equal and the hypotenuse is √2 times one leg, giving sin 45°=cos 45°=√2/2 and tan 45°=1. This symmetry is central to many trigonometric ratios practice scenarios and helps you ace the special angles trigonometry quiz questions. Referencing official math curriculum standards confirms its reliability.

  4. SOH-CAH-TOA Mnemonic and Practice -

    Apply SOH-CAH-TOA ("Sine=Opposite/Hypotenuse, Cosine=Adjacent/Hypotenuse, Tangent=Opposite/Adjacent") as your go-to mnemonic for quiz trigonometric ratios on special angles. Pair this with quick mental checks - like "S over H for sugar over honey" - to lock in formulas under timed conditions. Research from educational journals shows mnemonics boost retention by up to 30% in trigonometry learning.

  5. Complementary Angle Relationships -

    Leverage the identity sin θ=cos (90° - θ) and tan θ=cot (90° - θ) to convert between trigonometric ratios and reduce errors on a special angles trigonometry quiz. For example, sin 60° equals cos 30°, which can simplify multi-step questions in a quiz trigonometric ratios challenge. Official exam prep guides recommend using these relationships to cross-verify answers quickly.

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