Trigonometry Quiz
Trigonometry connects angles with side lengths in triangles. The quiz covers sine, cosine and tangent, standard angle values, identities and simple applications.
What this quiz covers
- Sine, cosine and tangent
- Standard angle values
- Trigonometric identities
- Heights and distances
Study tip: Memorise the values for 0°, 30°, 45°, 60° and 90° once; they appear in a large share of questions.
Questions, answers and explanations
1. What is the value of sin 90°?
- 0
- 1
- 1/2
- √3/2
Answer: 1
The value of sin 90° is 1.
2. What is the value of cos 0°?
- 0
- 1
- 1/2
- √3/2
Answer: 1
The value of cos 0° is 1.
3. What is the value of tan 45°?
- 0
- 1
- √3
- Undefined
Answer: 1
The value of tan 45° is 1.
4. Which side is opposite the right angle in a right triangle?
- Adjacent
- Base
- Hypotenuse
- Perpendicular
Answer: Hypotenuse
The hypotenuse is always opposite the right angle.
5. SOH stands for:
- Sin = Opposite / Hypotenuse
- Sin = Hypotenuse / Opposite
- Sin = Adjacent / Hypotenuse
- Sin = Opposite / Adjacent
Answer: Sin = Opposite / Hypotenuse
SOHCAHTOA: SOH means Sin = Opposite ÷ Hypotenuse.
6. What is the value of cos 90°?
- 0
- 1
- -1
- 1/2
Answer: 0
The value of cos 90° is 0.
7. What is the value of sin 30°?
- 1
- 1/2
- √3/2
- 0
Answer: 1/2
The value of sin 30° is 1/2.
8. What is the value of cos 60°?
- 1
- 1/2
- √3/2
- 0
Answer: 1/2
The value of cos 60° is 1/2.
9. Tangent is equal to:
- Sin / Cos
- Cos / Sin
- Hypotenuse / Opposite
- Adjacent / Opposite
Answer: Sin / Cos
tanθ = sinθ ÷ cosθ.
10. What is the value of tan 0°?
- 0
- 1
- Undefined
- -1
Answer: 0
The value of tan 0° is 0.
11. What is the value of sin 0°?
- 0
- 1
- 1/2
- √3/2
Answer: 0
The value of sin 0° is 0.
12. What is the value of tan 90°?
- 0
- 1
- Undefined
- -1
Answer: Undefined
tanθ = sinθ / cosθ. Since cos 90° = 0, tan 90° is undefined.
13. CAH stands for:
- Cos = Adjacent / Hypotenuse
- Cos = Opposite / Hypotenuse
- Cos = Opposite / Adjacent
- Cos = Hypotenuse / Adjacent
Answer: Cos = Adjacent / Hypotenuse
CAH in SOHCAHTOA means Cos = Adjacent ÷ Hypotenuse.
14. TOA stands for:
- Tan = Opposite / Adjacent
- Tan = Adjacent / Opposite
- Tan = Hypotenuse / Opposite
- Tan = Opposite / Hypotenuse
Answer: Tan = Opposite / Adjacent
TOA means Tan = Opposite ÷ Adjacent.
15. Which trigonometric ratio uses the adjacent side and the hypotenuse?
- Sine
- Cosine
- Tangent
- Cotangent
Answer: Cosine
Cosine is defined as Adjacent ÷ Hypotenuse.
16. What is the value of cos 180°?
- 1
- 0
- -1
- 1/2
Answer: -1
The value of cos 180° is -1.
17. What is the value of sin 180°?
- 0
- 1
- -1
- 1/2
Answer: 0
The value of sin 180° is 0.
18. Which trigonometric ratio is equal to Opposite ÷ Hypotenuse?
- Cosine
- Tangent
- Sine
- Secant
Answer: Sine
Sine = Opposite ÷ Hypotenuse.
19. If sin θ = 1, then θ is:
- 0°
- 30°
- 45°
- 90°
Answer: 90°
The sine of 90° is equal to 1.
20. Which theorem is commonly used with trigonometry in right triangles?
- Binomial Theorem
- Pythagoras Theorem
- Euclid's Theorem
- Newton's Theorem
Answer: Pythagoras Theorem
Pythagoras Theorem is widely used with trigonometric ratios in right triangles.