Introduction to Trigonometry Quiz

Grade 9 · Math · Quiz

Test your knowledge of sine, cosine, tangent, SOH-CAH-TOA, and special angles.

Questions

What does cos(θ) equal in a right triangle?
1. opposite / adjacent
2. adjacent / hypotenuse
3. opposite / hypotenuse
4. hypotenuse / adjacent
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Answer: adjacent / hypotenuse
cos(θ) = adjacent / hypotenuse — the 'C' in CAH.
sin(30°) = 0.5
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Answer: True
sin(30°) = 1/2 = 0.5 — a standard special angle value.
In a right triangle, the side next to the reference angle (not the hypotenuse) is called the:
1. opposite
2. adjacent
3. hypotenuse
4. leg
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Answer: adjacent
The adjacent side is next to the reference angle but is not the hypotenuse.
cos(60°) = ___.
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Answer: 1/2
cos(60°) = 1/2 is a standard special angle value.
A right triangle has opposite = 4 and hypotenuse = 5. What is sin(θ)?
1. 4/5
2. 3/5
3. 5/4
4. 5/3
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Answer: 4/5
sin(θ) = opposite/hypotenuse = 4/5.
The tangent of 90° is defined.
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Answer: False
tan(90°) = sin(90°)/cos(90°) = 1/0, which is undefined.
A right triangle has angle 45° and adjacent = 7. What is the opposite side?
1. 7
2. 14
3. 7√2
4. 3.5
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Answer: 7
tan(45°) = 1, so opposite = adjacent × 1 = 7.
To find an unknown angle when you know two sides, you use an ___ trig function.
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Answer: inverse
Inverse functions sin⁻¹, cos⁻¹, tan⁻¹ return the angle from a known ratio.
What is tan(30°)?
1. √3
2. 1/√3
3. 1
4. 1/2
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Answer: 1/√3
tan(30°) = sin(30°)/cos(30°) = (1/2)/(√3/2) = 1/√3 ≈ 0.577.
A ramp rises 3 m over a horizontal distance of 4 m. What is the tangent of the angle of elevation?
1. 3/4
2. 4/3
3. 3/5
4. 4/5
Show answer
Answer: 3/4
tan(angle) = opposite/adjacent = rise/run = 3/4.

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