Trigonometry Quizzes: Master Trig Functions, Identities, and Triangle Applications

Question 1

Given cos(α) = 0.8, find the value of α.

Accepted Answer

30°

Answer

45°

Answer

60°

Answer

90°

Question 2

Identify the inverse function of y = sin(x).

Accepted Answer

y = arcsin(x)

Answer

y = cos(x)

Answer

y = tan(x)

Answer

y = cot(x)

Question 3

Which equation qualifies as a trigonometric inequality?

Accepted Answer

sin(x) < 0

Answer

cos(x) = 3

Answer

tan(x) - 2 = 0

Answer

cot(x) + 4 = 6

Question 4

Which of the following is the Pythagorean identity for trigonometry?

Accepted Answer

sin² θ + cos² θ = 1

Answer

tan θ = sin θ / cos θ

Answer

cot θ = cos θ / sin θ

Answer

sec θ = 1 / cos θ

Question 5

Compute the derivative of the function y = tan x.

Accepted Answer

sec² x

Answer

cos² x / sin² x

Answer

sin x / cos x

Answer

cot x

Question 6

A surveyor measures the angle of elevation from a point 50 meters away from the base of a tree to be 30 degrees. What is the height of the tree?

Accepted Answer

25 meters

Answer

50 meters

Answer

75 meters

Answer

100 meters

Question 7

Consider a right triangle with an angle of 30 degrees. What is the value of the cosine of this angle?

Accepted Answer

0.5

Answer

0.75

Answer

1.0

Answer

1.25

Question 8

Which of the following is NOT a Pythagorean identity?

Accepted Answer

cosec^2 x - cot^2 x = 1

Answer

sin^2 x + cos^2 x = 1

Answer

tan^2 x + 1 = sec^2 x

Answer

cot^2 x - 1 = cosec^2 x

Question 9

Which of the following is the inverse function of the sine function?

Accepted Answer

Arcsine

Answer

Cosine

Answer

Tangent

Answer

Cotangent

Question 10

Find the period of the function f(x) = 2sin(3x).

Accepted Answer

2π/3

Answer

π/2

Answer

π/3

Answer

3π/2

Question 11

Which of the following graphs represents the function y = cos x?

Accepted Answer

[Image of a cosine graph]

Answer

[Image of a sine graph]

Answer

[Image of a tangent graph]

Answer

[Image of a cotangent graph]

Question 12

What is the amplitude of the function f(x) = -3cos(2x + π/4)?

Accepted Answer

3

Answer

1

Answer

2

Answer

4

Question 13

Which of the following vectors is NOT a unit vector?

Accepted Answer

(2, 3, 4)

Answer

(0, 1, 0)

Answer

(1, 0, 0)

Answer

(0, 0, 1)

Question 14

Which of the following formulas represents the surface area of a cylinder?

Accepted Answer

2πrh + 2πr²

Answer

πr²h

Answer

πr² + 2πrh

Answer

4πr²h

Question 15

What is the inverse function of the sine function called?

Accepted Answer

Arcsine

Answer

Cosecant

Answer

Cosine

Answer

Tangent

Question 16

Which of the following is not a quadrant in a coordinate plane?

Accepted Answer

Quadrant V

Answer

Quadrant II

Answer

Quadrant III

Answer

Quadrant I

Question 17

Which formula represents the Law of Sines?

Accepted Answer

a/sin(A) = b/sin(B) = c/sin(C)

Answer

tan(A/2) = (a - b) / (a + b)

Answer

a² + b² = c²

Answer

cos(A) + cos(B) + cos(C) = 0

Question 18

What is the range of the cosine function?

Accepted Answer

[-1, 1]

Answer

[1, ∞]

Answer

[0, 1]

Answer

[-∞, ∞]

Question 19

A ladder 10 meters long leans against a wall. If the foot of the ladder is 6 meters from the wall, what is the angle the ladder makes with the ground? (Round your answer to two decimal places.)

Accepted Answer

53.13°

Answer

45°

Answer

36.87°

Question 20

Which of the following is the correct expression for the sine of the sum of two angles?

Accepted Answer

sin(A + B) = sinA cosB + cosA sinB

Answer

sin(A + B) = sinA cosB - cosA sinB

Answer

sin(A + B) = cosA cosB - sinA sinB

Question 21

What is the general solution to the equation sinθ = 0?

Accepted Answer

θ = nπ, where n is an integer

Answer

θ = π/2 + 2nπ, where n is an integer

Answer

θ = 2nπ, where n is an integer

Question 22

A right triangle has an angle of 30 degrees and a hypotenuse of length 10 cm. What is the length of the side opposite the 30-degree angle?

Accepted Answer

5 cm

Answer

5√3 cm

Question 23

Which of the following is equivalent to sin(x + π/2)?

Accepted Answer

cos(x)

Answer

-cos(x)

Answer

-sin(x)

Question 24

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

Accepted Answer

2π/3

Answer

3π

Question 25

A ladder leans against a wall, making a 60-degree angle with the ground. If the ladder is 5 meters long, how far is the base of the ladder from the wall?

Accepted Answer

2.5 meters

Answer

5 meters

Question 26

Which of the following is NOT a trigonometric identity?

Accepted Answer

sin(x) + cos(x) = 1

Answer

sin²(x) + cos²(x) = 1

Answer

tan(x) = sin(x)/cos(x)

Question 27

What is the range of the function y = arcsin(x)?

Accepted Answer

-π/2 ≤ y ≤ π/2

Answer

-∞ < y < ∞

Question 28

Two sides of a triangle have lengths 5 cm and 8 cm, and the included angle is 60 degrees. What is the area of the triangle?

Accepted Answer

10√3 cm²

Answer

20 cm²

Question 29

Which of the following is the graph of y = tan(x)?

Accepted Answer

(Image of the graph of y = tan(x))

Answer

(Image of the graph of y = sin(x))

Answer

(Image of the graph of y = cos(x))

Question 30

Convert 135 degrees to radians.

Accepted Answer

3π/4

Answer

π/4

Answer

7π/4

Answer

5π/4

Question 31

A ship sails 30 km due north and then 40 km due east. What is the bearing of the ship from its starting point?

Accepted Answer

arctan(4/3) + 90 degrees

Answer

arctan(4/3)

Answer

arctan(3/4) + 90 degrees

Answer

arctan(3/4)