1. What is sin 30°?
- A
- B
- C1
- D
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Answer: A)
Standard value: sin 30° = .
Class 10 Introduction to Trigonometry — practice questions with answers
Trigonometry · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.
2. Evaluate 2 sin 30° + 3 cos 60°.
- A
- B1
- C
- D5
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Answer: A)
.
3. If cos θ = (acute θ), find the value of θ.
- A30°
- B45°
- C60°
- D90°
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Answer: A) 30°
cos 30° = , so θ = 30°.
4. Evaluate: sin²60° + cos²45° − tan²30°.
- A
- B
- C
- D1
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Answer: A)
sin²60° = , cos²45° = , tan²30° = . Using twelfths: .
5. As θ increases from 0° towards 90°, the value of tan θ:
- Adecreases steadily from 1 to 0
- Bincreases from 0 up to 1 and stops there
- Cstays constant at 1 throughout
- Dincreases from 0 and grows without any upper limit, and is undefined at 90°
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Answer: D) increases from 0 and grows without any upper limit, and is undefined at 90°
tan θ = . As θ grows, sin θ rises towards 1 while cos θ falls towards 0, so the ratio keeps getting larger (tan 45° = 1, tan 60° = ≈ 1.73, tan 89° ≈ 57). At 90° the denominator is 0, so tan 90° is undefined.
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