Q.1 If sin θ = 3/5, what is cos θ (θ is acute)?
4/5
3/4
5/4
12/13
Explanation - Using Pythagoras theorem: cos θ = √(1 - sin²θ) = √(1 - (9/25)) = √(16/25) = 4/5.
Correct answer is: 4/5
Q.2 If cos θ = 12/13, what is sin θ (θ acute)?
5/13
12/13
13/5
1/2
Explanation - sin²θ = 1 - cos²θ = 1 - (144/169) = 25/169. So sin θ = 5/13.
Correct answer is: 5/13
Q.3 The value of tan 45° is:
0
1
√3
∞
Explanation - tan 45° = sin 45° / cos 45° = (√2/2) / (√2/2) = 1.
Correct answer is: 1
Q.4 Which of the following is equal to sec θ?
1/cos θ
1/sin θ
1/tan θ
sin θ
Explanation - By definition, sec θ = 1 / cos θ.
Correct answer is: 1/cos θ
Q.5 If tan θ = 3/4, find sin θ (θ acute).
3/5
4/5
5/3
5/4
Explanation - tan θ = sin θ / cos θ = 3/4. Hypotenuse = 5, opposite = 3, adjacent = 4. So sin θ = 3/5.
Correct answer is: 3/5
Q.6 The reciprocal of cosec θ is:
sin θ
cos θ
sec θ
cot θ
Explanation - cosec θ = 1/sin θ, so its reciprocal is sin θ.
Correct answer is: sin θ
Q.7 If sin θ = 1/2, then θ (acute) is:
30°
45°
60°
90°
Explanation - sin 30° = 1/2, hence θ = 30°.
Correct answer is: 30°
Q.8 The value of cos 60° is:
0
1
1/2
√3/2
Explanation - cos 60° = 1/2 is a standard trigonometric ratio.
Correct answer is: 1/2
Q.9 If cos θ = 4/5, then tan θ = ?
3/4
4/3
5/4
3/5
Explanation - sin θ = √(1 - cos²θ) = 3/5. tan θ = sin θ / cos θ = (3/5) / (4/5) = 3/4.
Correct answer is: 3/4
Q.10 sin²θ + cos²θ is equal to:
0
1
2
sin θ cos θ
Explanation - Pythagorean identity states sin²θ + cos²θ = 1.
Correct answer is: 1
Q.11 The value of cosec 90° is:
0
1
∞
Not defined
Explanation - sin 90° = 1, so cosec 90° = 1/sin 90° = 1.
Correct answer is: 1
Q.12 The value of tan 0° is:
0
1
∞
Not defined
Explanation - tan 0° = sin 0° / cos 0° = 0/1 = 0.
Correct answer is: 0
Q.13 If cos θ = 0, then θ = ?
0°
45°
90°
180°
Explanation - cos 90° = 0.
Correct answer is: 90°
Q.14 If sin θ = 5/13, find cos θ (θ acute).
12/13
5/12
13/5
1/2
Explanation - cos²θ = 1 - sin²θ = 1 - 25/169 = 144/169 → cos θ = 12/13.
Correct answer is: 12/13
Q.15 The value of cos 0° is:
0
1
√3/2
1/2
Explanation - cos 0° = 1 by definition.
Correct answer is: 1
Q.16 If tan θ = 1, then θ (acute) is:
30°
45°
60°
90°
Explanation - tan 45° = 1, so θ = 45°.
Correct answer is: 45°
Q.17 sec²θ - tan²θ = ?
0
1
sin θ
cos θ
Explanation - Trigonometric identity: sec²θ - tan²θ = 1.
Correct answer is: 1
Q.18 The value of sin 90° is:
0
1
-1
∞
Explanation - sin 90° = 1 by standard ratio.
Correct answer is: 1
Q.19 The reciprocal of sec θ is:
cos θ
sin θ
tan θ
cosec θ
Explanation - sec θ = 1/cos θ, so reciprocal is cos θ.
Correct answer is: cos θ
Q.20 If cos θ = 0.6, then sin θ = ? (θ acute)
0.8
0.5
0.4
0.3
Explanation - sin²θ = 1 - cos²θ = 1 - 0.36 = 0.64 → sin θ = 0.8.
Correct answer is: 0.8
Q.21 tan θ is equal to:
sin θ / cos θ
cos θ / sin θ
1 / sin θ
1 / cos θ
Explanation - By definition, tan θ = sin θ / cos θ.
Correct answer is: sin θ / cos θ
Q.22 The value of cos 90° is:
0
1
∞
Not defined
Explanation - cos 90° = 0.
Correct answer is: 0
Q.23 If cot θ = 1/√3, then θ = ?
30°
45°
60°
90°
Explanation - cot θ = cos θ / sin θ. If cot θ = 1/√3, tan θ = √3 → θ = 60°.
Correct answer is: 60°
Q.24 If sin θ = cos θ, then θ = ? (acute)
30°
45°
60°
90°
Explanation - At θ = 45°, sin θ = cos θ = √2/2.
Correct answer is: 45°
Q.25 The value of tan 90° is:
0
1
∞
Not defined
Explanation - tan θ = sin θ / cos θ. At θ = 90°, cos θ = 0 → undefined.
Correct answer is: Not defined