Q.1 If sin A = 3/5, find cos A, assuming A is in the first quadrant.
4/5
5/3
3/4
2/5
Explanation - Using sin²A + cos²A = 1, cos A = √(1 - sin²A) = √(1 - 9/25) = √(16/25) = 4/5.
Correct answer is: 4/5
Q.2 Find the value of tan 45°.
1
0
√2
√3
Explanation - tan θ = sin θ / cos θ. For θ = 45°, sin 45° = cos 45° = √2/2, so tan 45° = 1.
Correct answer is: 1
Q.3 If cos θ = 12/13 and θ is in the first quadrant, find sin θ.
5/13
12/13
13/12
5/12
Explanation - Using sin²θ + cos²θ = 1, sin θ = √(1 - (12/13)²) = √(1 - 144/169) = √(25/169) = 5/13.
Correct answer is: 5/13
Q.4 The value of sin²30° + cos²60° is:
1
1/2
0
3/4
Explanation - sin 30° = 1/2 ⇒ sin²30° = 1/4, cos 60° = 1/2 ⇒ cos²60° = 1/4. Sum = 1/4 + 1/4 = 1/2 (Oops, recalc) Actually: sin²30° + cos²60° = 1/4 + 1/4 = 1/2
Correct answer is: 1
Q.5 If tan A = 1, then the value of sin²A + cos²A is:
1
0
2
1/2
Explanation - sin²A + cos²A = 1 for any angle A.
Correct answer is: 1
Q.6 Find the value of cos 0°.
1
0
-1
Undefined
Explanation - cos 0° = 1 by definition.
Correct answer is: 1
Q.7 The value of sin 90° is:
1
0
-1
Undefined
Explanation - By definition, sin 90° = 1.
Correct answer is: 1
Q.8 If sin A = 4/5 and A is in the first quadrant, find tan A.
4/3
3/4
5/4
4/5
Explanation - cos A = √(1 - sin²A) = 3/5, so tan A = sin A / cos A = (4/5)/(3/5) = 4/3.
Correct answer is: 4/3
Q.9 Find the principal value of sin⁻¹(1/2).
30°
45°
60°
90°
Explanation - sin 30° = 1/2, so principal value is 30°.
Correct answer is: 30°
Q.10 If sin²A = 3/4, find cos A (A in first quadrant).
1/2
√3/2
√2/2
3/4
Explanation - cos²A = 1 - sin²A = 1 - 3/4 = 1/4 ⇒ cos A = 1/2.
Correct answer is: 1/2
Q.11 Find sin 2A if sin A = 3/5 and cos A = 4/5.
24/25
3/5
4/5
7/25
Explanation - sin 2A = 2 sin A cos A = 2 * 3/5 * 4/5 = 24/25.
Correct answer is: 24/25
Q.12 If cos²θ = 1/2, then θ in the first quadrant is:
45°
30°
60°
90°
Explanation - cos θ = √(1/2) = 1/√2 ⇒ θ = 45°.
Correct answer is: 45°
Q.13 Find the value of cos 180°.
-1
0
1
Undefined
Explanation - By definition, cos 180° = -1.
Correct answer is: -1
Q.14 If sin A = 5/13 and A is in the first quadrant, find sec A.
13/12
13/5
12/5
5/12
Explanation - cos A = √(1 - sin²A) = √(1 - 25/169) = 12/13 ⇒ sec A = 1/cos A = 13/12.
Correct answer is: 13/12
Q.15 The value of tan 60° is:
√3
1/√3
1
√2
Explanation - tan θ = sin θ / cos θ = (√3/2)/(1/2) = √3.
Correct answer is: √3
Q.16 If cos A = 3/5 and sin A > 0, find cot A.
3/4
4/3
5/3
3/5
Explanation - sin A = √(1 - 9/25) = 4/5 ⇒ cot A = cos A / sin A = (3/5)/(4/5) = 3/4.
Correct answer is: 3/4
Q.17 If sin θ = 1/√2, find θ in the first quadrant.
45°
30°
60°
90°
Explanation - sin θ = 1/√2 ⇒ θ = 45° in the first quadrant.
Correct answer is: 45°
Q.18 If sin A = cos B, then A + B = ?
90°
180°
45°
60°
Explanation - sin A = cos B ⇒ sin A = sin(90° - B) ⇒ A = 90° - B ⇒ A + B = 90°.
Correct answer is: 90°
Q.19 The value of cos 90° is:
0
1
-1
Undefined
Explanation - cos 90° = 0 by definition.
Correct answer is: 0
Q.20 If sin θ = 0, then θ could be:
0°
30°
45°
60°
Explanation - sin θ = 0 ⇒ θ = 0°, 180°, 360°, ... in general.
Correct answer is: 0°
Q.21 Find the value of sin 180°.
0
1
-1
Undefined
Explanation - sin 180° = 0 by definition.
Correct answer is: 0
Q.22 If sin A = 2/3, find cos²A.
5/9
4/9
1/9
2/3
Explanation - cos²A = 1 - sin²A = 1 - 4/9 = 5/9.
Correct answer is: 5/9
Q.23 If sin²A + cos²A = 1, what is sin²A if cos²A = 9/16?
7/16
9/16
1/16
8/16
Explanation - sin²A = 1 - cos²A = 1 - 9/16 = 7/16.
Correct answer is: 7/16
Q.24 Find the value of tan 30°.
1/√3
√3
1
√2
Explanation - tan θ = sin θ / cos θ = (1/2)/(√3/2) = 1/√3.
Correct answer is: 1/√3
Q.25 If cos A = 0, then A is:
90°
0°
45°
60°
Explanation - cos A = 0 ⇒ A = 90° or 270°; first quadrant gives 90°.
Correct answer is: 90°