Master Trigonometry for Engineering: Online Quizzes and Practice

Question 1

Which trigonometric ratio is used to determine the length of the adjacent side in a right-angled triangle?

Accepted Answer

Cosine

Answer

Sine

Answer

Tangent

Question 2

From a point A, the angle of elevation to the top of a building is 30°. If the building is 100 meters tall, what is the horizontal distance between point A and the base of the building?

Accepted Answer

50√3 meters

Answer

100√3 meters

Answer

50/√3 meters

Question 3

Which trigonometric identity holds true for all angles?

Accepted Answer

sin²x + cos²x = 1

Answer

tanx = sinx/cosx

Answer

cotx + tanx = 1

Question 4

What is the period of the trigonometric function y = sin(2x)?

Accepted Answer

2π

Answer

π

Answer

π/2

Question 5

In a right-angled triangle, the hypotenuse measures 10 units and the opposite side measures 6 units. What is the sine of the angle opposite the 6-unit side?

Accepted Answer

3/5

Answer

5/3

Answer

6/10

Question 6

What is the amplitude of the trigonometric function y = 2cos(3x)?

Accepted Answer

2

Answer

1

Answer

3

Question 7

In a circle with a radius of 5 units, if the central angle measures 60 degrees, what is the length of the arc intercepted by the central angle?

Accepted Answer

5π/3

Answer

2.5π

Answer

π/3

Question 8

If the sine of an angle is 0.7, what is the cosine of that angle?

Accepted Answer

0.8

Answer

0.6

Answer

0.9

Answer

0.5

Question 9

What is the period of the trigonometric function f(x) = sin(2x)?

Accepted Answer

2π

Answer

π

Answer

π/2

Answer

π/4

Question 10

What is the amplitude of the trigonometric function f(x) = 2cos(x)?

Accepted Answer

2

Answer

1

Answer

3

Answer

4

Question 11

What is the range of the trigonometric function f(x) = tan(x)?

Accepted Answer

[-∞, ∞]

Answer

[-1, 1]

Answer

[0, ∞]

Answer

[1, ∞]

Question 12

Use the trigonometric identity sin^2(x) + cos^2(x) = 1 to derive the identity tan^2(x) + 1 = sec^2(x).

Accepted Answer

Yes, squaring both sides of the equation preserves its validity.

Answer

No, squaring both sides of the equation may introduce extraneous solutions.

Answer

Yes, but only if the angle x is limited to the first quadrant.

Question 13

In a right-angled triangle, which trigonometric ratio is defined as the ratio of the length of the opposite side to the length of the hypotenuse?

Accepted Answer

Sine

Answer

Cosine

Answer

Tangent

Answer

Cotangent

Question 14

What is the value of sin(30°) ?

Accepted Answer

0.707

Answer

0.5

Answer

1

Answer

2

Question 15

Convert 45° to radians.

Accepted Answer

π / 4

Answer

π / 2

Answer

π / 6

Answer

π / 8

Question 16

Which of the following graphs accurately represents the function y = sin(x)?

Accepted Answer

A sinusoidal graph

Answer

A linear graph

Answer

A parabolic graph

Answer

A circular graph

Question 17

Determine the period of the function y = cos(2x).

Accepted Answer

2π

Answer

π

Answer

π / 2

Answer

4π

Question 18

In a right-angled triangle, which trigonometric ratio represents the length of the side opposite the angle to the length of the hypotenuse?

Accepted Answer

Sine

Answer

Cosine

Answer

Tangent

Answer

Cosecant

Question 19

Using the unit circle, evaluate the sine of 30 degrees.

Accepted Answer

0.707

Answer

0.5

Answer

1.0

Answer

1.732

Question 20

A ladder leans against a wall, with its base 4 meters from the wall and its top reaching a height of 3 meters on the wall. Calculate the angle of elevation of the ladder.

Accepted Answer

53°

Answer

37°

Answer

45°

Answer

60°

Question 21

What is the domain of the tangent function?

Accepted Answer

All real numbers except multiples of π/2

Answer

All real numbers

Answer

All real numbers except zero

Answer

All positive real numbers

Question 22

In a right-angled triangle, the ratio of the length of the side opposite the 30-degree angle to the length of the hypotenuse is called:

Accepted Answer

Sine

Answer

Cosine

Answer

Tangent

Answer

Cotangent

Question 23

Which identity relates the sine and cosine functions?

Accepted Answer

sin² θ + cos² θ = 1

Answer

tan² θ + cot² θ = 1

Answer

sec² θ - 1 = tan² θ

Answer

cosec² θ - 1 = tan² θ

Question 24

What is the exact value of tan 45°?

Accepted Answer

1

Answer

0

Answer

√2

Answer

2

Question 25

Which of the following expressions is equivalent to sin θ cos θ?

Accepted Answer

1/2 sin 2θ

Answer

tan θ

Answer

cot θ

Answer

1/2 cos 2θ

Question 26

Which graph represents the function y = cos(x) + 1?

Accepted Answer

A cosine curve shifted up by 1 unit.

Answer

A sine curve shifted up by 1 unit.

Answer

A sine curve shifted down by 1 unit.

Answer

A cosine curve shifted down by 1 unit.

Question 27

The derivative of the function y = tan x is:

Accepted Answer

sec² x

Answer

csc² x

Answer

cot² x

Answer

cosec² x

Question 28

The area of a sector of a circle with radius r and central angle θ is given by:

Accepted Answer

1/2 πr²θ

Answer

πr²θ

Answer

r²θ

Answer

1/2 r²θ

Question 29

Which of the following is not a trigonometric ratio?

Accepted Answer

Quadrant

Answer

Cosine

Answer

Sine

Answer

Tangent

Question 30

What is the value of the tangent of 45°?

Accepted Answer

1

Answer

0

Answer

undefined

Answer

2

Question 31

Which of the following identities is used to find the missing side of a right triangle?

Accepted Answer

Pythagorean Theorem (a^2 + b^2 = c^2)

Answer

Law of Cosines

Answer

Sine Law

Answer

Law of Sines

Question 32

Which of the following is the inverse function of sin(x)?

Accepted Answer

arcsin(x)

Answer

tan(x)

Answer

csc(x)

Answer

cos(x)

Question 33

Calculate the value of sin(π/3):

Accepted Answer

√3/2

Answer

√2/2

Answer

1/2

Answer

0

Question 34

Which of the following is a fundamental trigonometric identity?

Accepted Answer

sin²θ + cos²θ = 1

Answer

sinθ = tanθ

Answer

cosθ = 1/sinθ

Question 35

Determine the range of values for the cotangent function:

Accepted Answer

(-∞, ∞)

Answer

(-π/2, π/2)

Answer

(-1, 1)

Answer

(0, ∞)

Question 36

Find the principal value of tan⁻¹(1):

Accepted Answer

π/4

Answer

0

Answer

π

Answer

π/2

Question 37

Which trigonometric identity is equivalent to the expression 1 + tan^2(x) = sec^2(x)?

Accepted Answer

Pythagorean Identity

Answer

Half-Angle Identity

Answer

Double-Angle Identity

Answer

Sum-to-Product Identity

Question 38

In a triangle with sides a, b, and c, and angles A, B, and C, which law relates the lengths of the sides to the cosines of the opposite angles?

Accepted Answer

Law of Cosines

Answer

Pythagorean Theorem

Answer

Law of Sines

Question 39

What is the domain of the tangent function?

Accepted Answer

All real numbers except odd multiples of π/2

Answer

All angles between 0 and 2π

Answer

All positive real numbers

Answer

All real numbers

Question 40

Determine the formula for calculating the area of a triangle with sides a, b, and c and semiperimeter s:

Accepted Answer

√s(s - a)(s - b)(s - c)

Answer

1/2(ab + bc + ca)

Answer

1/2ab sin(C)

Question 41

What is the inverse function of the cosine function?

Accepted Answer

Arccosine

Answer

Tangent

Answer

Sine

Answer

Secant