Trigonometry Study Resources for Competitive Exams

Trigonometry

Heights & Distances Identities Multiple & Sub-Multiple Angles Trigonometric Ratios

Q. If a = 1 and b = 4, what is the value of a³ + b³?

A. 65
B. 65
C. 125
D. 125

Solution

a³ + b³ = 1³ + 4³ = 1 + 64 = 65.

Correct Answer: A — 65

Learn More →

Q. If a = 2 and b = 3, what is the value of (a + b)² - (a² + b²)?

A. 0
B. 2
C. 4
D. 6

Solution

(a + b)² = (2 + 3)² = 25; a² + b² = 2² + 3² = 4 + 9 = 13; thus, 25 - 13 = 12.

Correct Answer: C — 4

Learn More →

Q. If a = 2 and b = 3, what is the value of (a + b)²?

A. 25
B. 30
C. 20
D. 15

Solution

(a + b)² = (2 + 3)² = 5² = 25.

Correct Answer: A — 25

Learn More →

Q. If a = 2 and b = 5, what is the value of (a + b)²?

A. 49
B. 25
C. 36
D. 64

Solution

(a + b)² = (2 + 5)² = 7² = 49.

Correct Answer: A — 49

Learn More →

Q. If a = 2 and b = 5, what is the value of a² + 2ab + b²?

A. 49
B. 25
C. 36
D. 64

Solution

a² + 2ab + b² = 2² + 2*2*5 + 5² = 4 + 20 + 25 = 49.

Correct Answer: A — 49

Learn More →

Q. If a = 3 and b = 4, what is the value of a² + b²?

A. 7
B. 12
C. 25
D. 34

Solution

a² + b² = 3² + 4² = 9 + 16 = 25.

Correct Answer: C — 25

Learn More →

Q. If a = 3 and b = 5, what is the value of a² + b² - 2ab?

A. -1
B. 1
C. 0
D. 2

Solution

a² + b² - 2ab = 3² + 5² - 2(3)(5) = 9 + 25 - 30 = 4.

Correct Answer: B — 1

Learn More →

Q. If a = 4 and b = 5, what is the value of a² + b²?

A. 41
B. 25
C. 16
D. 9

Solution

a² + b² = 4² + 5² = 16 + 25 = 41.

Correct Answer: A — 41

Learn More →

Q. If a = 5 and b = 2, what is the value of (a - b)²?

A. 9
B. 25
C. 49
D. 1

Solution

(a - b)² = (5 - 2)² = 3² = 9.

Correct Answer: A — 9

Learn More →

Q. If a = 5 and b = 4, what is the value of (a + b)²?

A. 81
B. 90
C. 100
D. 64

Solution

(a + b)² = (5 + 4)² = 9² = 81.

Correct Answer: C — 100

Learn More →

Q. If a person standing 30 m away from a building observes the top of the building at an angle of elevation of 60 degrees, what is the height of the building? (2023)

A. 15 m
B. 25 m
C. 30 m
D. 51.96 m

Solution

Height = distance * tan(60) = 30 * √3 ≈ 30 * 1.732 = 51.96 m.

Correct Answer: D — 51.96 m

Learn More →

Q. If cos A = 5/13, what is the value of tan A?

A. 12/5
B. 5/12
C. 13/5
D. 5/13

Solution

Using the identity tan A = sin A / cos A, we find sin A = √(1 - cos²A) = √(1 - (5/13)²) = 12/13. Thus, tan A = (12/13) / (5/13) = 12/5.

Correct Answer: A — 12/5

Learn More →

Q. If cos B = 0.6, what is the value of sin B?

A. 0.8
B. 0.6
C. 0.4
D. 0.2

Solution

Using the Pythagorean identity, sin B = √(1 - cos²B) = √(1 - 0.6²) = √(1 - 0.36) = √(0.64) = 0.8.

Correct Answer: A — 0.8

Learn More →

Q. If cos B = 1/2, what is the value of angle B in degrees?

A. 30°
B. 60°
C. 90°
D. 120°

Solution

Cosine of 60° is 1/2, hence angle B = 60°.

Correct Answer: B — 60°

Learn More →

Q. If cos B = 5/13, what is the value of sin B?

A. 12/13
B. 5/13
C. 13/5
D. 3/5

Solution

Using the Pythagorean identity, sin B = √(1 - cos²B) = √(1 - (5/13)²) = √(1 - 25/169) = √(144/169) = 12/13.

Correct Answer: A — 12/13

Learn More →

Q. If cos C = 0.5, what is the value of angle C in degrees?

A. 30
B. 60
C. 90
D. 45

Solution

The angle C for which cos C = 0.5 is 60°.

Correct Answer: B — 60

Learn More →

Q. If cot A = 1, what is the value of A? (2022)

A. 45°
B. 90°
C. 60°
D. 30°

Solution

Cotangent is 1 when the angle A is 45°, as cot A = cos A/sin A = 1 when both are equal.

Correct Answer: A — 45°

Learn More →

Q. If cot A = 3/4, what is the value of sin A?

A. 3/5
B. 4/5
C. 5/3
D. 5/4

Solution

cot A = cos A/sin A = 3/4 implies sin A = 4/5 using the identity sin²A + cos²A = 1.

Correct Answer: A — 3/5

Learn More →

Q. If cot D = 3/4, what is the value of sin D?

A. 3/5
B. 4/5
C. 5/3
D. 5/4

Solution

cot D = 3/4 implies tan D = 4/3. Therefore, sin D = 4/5 (using the identity sin²D + cos²D = 1).

Correct Answer: A — 3/5

Learn More →

Q. If cot θ = 1, what is the value of θ?

A. 0°
B. 45°
C. 90°
D. 180°

Solution

cot θ = 1 implies tan θ = 1, which occurs at θ = 45°.

Correct Answer: B — 45°

Learn More →

Q. If sin 2A = 2 sin A cos A, what is the double angle formula for cosine?

A. cos 2A = cos²A - sin²A
B. cos 2A = 2 sin A cos A
C. cos 2A = sin²A - cos²A
D. cos 2A = 1 - 2 sin²A

Solution

The double angle formula for cosine is cos 2A = cos²A - sin²A.

Correct Answer: A — cos 2A = cos²A - sin²A

Learn More →

Q. If sin 2A = 2 sin A cos A, what is the value of sin 2A when sin A = 1/2?

A. 1/2
B. 1
C. √3/2
D. 0

Solution

Using the double angle formula, sin 2A = 2(1/2)(√(1 - (1/2)²)) = 2(1/2)(√(3/4)) = 1.

Correct Answer: B — 1

Learn More →

Q. If sin 2θ = 2 sin θ cos θ, what is the value of sin 2(30°)?

A. 0
B. 1/2
C. √3/2
D. 1

Solution

sin 2(30°) = sin 60° = √3/2.

Correct Answer: C — √3/2

Learn More →

Q. If sin A = 0, what is the value of A? (2019)

A. 0°
B. 90°
C. 180°
D. 360°

Solution

Sin A = 0 at A = 0°, 180°, and 360°. The principal value is 0°.

Correct Answer: A — 0°

Learn More →

Q. If sin A = 0.6, what is the value of cos A to two decimal places?

A. 0.8
B. 0.6
C. 0.4
D. 0.2

Solution

Using the Pythagorean identity, cos A = √(1 - sin²A) = √(1 - 0.36) = √(0.64) = 0.8.

Correct Answer: A — 0.8

Learn More →

Q. If sin A = 0.8, what is the value of tan A?

A. 0.6
B. 1.2
C. 1.5
D. 0.8

Solution

Using the identity tan A = sin A / cos A. First, find cos A using cos A = √(1 - sin² A) = √(1 - 0.64) = 0.6. Therefore, tan A = 0.8 / 0.6 = 1.3333, which is approximately 1.2.

Correct Answer: B — 1.2

Learn More →

Q. If sin A = 1/2, what is the value of A in radians?

A. π/6
B. π/4
C. π/3
D. π/2

Solution

The angle A for which sin A = 1/2 is π/6 radians.

Correct Answer: A — π/6

Learn More →

Q. If sin A = 1/2, what is the value of A in the first quadrant?

A. 30°
B. 45°
C. 60°
D. 90°

Solution

In the first quadrant, sin A = 1/2 corresponds to A = 30°.

Correct Answer: A — 30°

Learn More →

Q. If sin A = 1/√2, what is the value of tan A?

A. 1
B. √2
C. 2
D. 1/2

Solution

tan A = sin A / cos A = (1/√2) / (1/√2) = 1.

Correct Answer: A — 1

Learn More →

Q. If sin A = 5/13, what is the value of cos A?

A. 12/13
B. 5/12
C. 13/5
D. 1/5

Solution

Using the Pythagorean identity, cos A = √(1 - sin²A) = √(1 - (5/13)²) = √(1 - 25/169) = √(144/169) = 12/13.

Correct Answer: A — 12/13

Learn More →

Showing 31 to 60 of 112 (4 Pages)

Trigonometry

On a scale of 0–10, how likely are you to recommend The Soulshift Academy?