Trigonometry Quizzes: Master Triangle Math Concepts

Question 1

In a right triangle, what is the ratio of the length of the hypotenuse to the length of the side adjacent to the right angle called?

Accepted Answer

Cosine

Answer

Sine

Answer

Tangent

Answer

Cotangent

Question 2

In a right triangle, the sine of an angle is defined as the ratio of the length of which side to the length of which side?

Accepted Answer

Opposite side to hypotenuse

Answer

Adjacent side to hypotenuse

Answer

Opposite side to adjacent side

Question 3

Which trigonometric function finds the ratio of the opposite side to the hypotenuse of a right triangle?

Accepted Answer

Sine

Answer

Tangent

Answer

Cosine

Answer

Cotangent

Question 4

What is the formula for the area of a triangle given its base and height?

Accepted Answer

Area = (1/2) * base * height

Answer

Area = (1/4) * base * height

Answer

Area = base * height

Answer

Area = 2 * base * height

Question 5

What is the value of sin(90 degrees)?

Accepted Answer

1

Answer

0

Answer

-1

Answer

√2/2

Question 6

In a unit circle, what are the coordinates of the point corresponding to an angle of -π/4?

Accepted Answer

(√2/2, -√2/2)

Answer

(-1, 0)

Answer

(0, 1)

Answer

(1, 0)

Question 7

What is the amplitude of the function f(x) = 3sin(2x)?

Accepted Answer

3

Answer

1

Answer

4

Answer

2

Question 8

State the Pythagorean Theorem formula.

Accepted Answer

a² + b² = c²

Answer

a² - b² = c²

Answer

c² - b² = a²

Answer

a² + c² = b²

Question 9

Which trigonometric function is defined as the ratio of the length of the opposite side to the length of the hypotenuse?

Accepted Answer

Sine

Answer

Cosine

Answer

Cotangent

Answer

Tangent

Question 10

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

Accepted Answer

3

Answer

2

Answer

1

Question 11

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

Accepted Answer

2π/3

Answer

π

Answer

3π/2

Question 12

The sine of an angle is defined as the ratio of the:

Accepted Answer

Length of the side opposite the angle to the length of the hypotenuse

Answer

Length of the adjacent side to the length of the hypotenuse

Answer

Length of the opposite side to the length of the adjacent side

Question 13

Which of the following trigonometric identities is correct?

Accepted Answer

sin²(x) + cos²(x) = 1

Answer

tan(x) = sin(x) + cos(x)

Answer

sin²(x) + cos²(x) = 2

Question 14

The Pythagorean Theorem states that in a right triangle, the square of the:

Accepted Answer

Length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides

Answer

Length of the opposite side is equal to the sum of the squares of the lengths of the other two sides

Answer

Length of the adjacent side is equal to the sum of the squares of the lengths of the other two sides

Question 15

The range of values of the tangent function is:

Accepted Answer

All real numbers

Answer

0 to 1

Answer

0 to π

Answer

-1 to 1

Question 16

Which of the following functions is the reciprocal of the cosine function?

Accepted Answer

Secant

Answer

Tangent

Answer

Sine

Question 17

The period of the sine function is:

Accepted Answer

2π

Answer

1

Answer

4π

Answer

π

Question 18

In a triangle with sides a, b, and c, and angles A, B, and C opposite to sides a, b, and c respectively, the Law of Sines states that:

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 19

A right triangle has a hypotenuse of 10 units and one leg of 6 units. What is the length of the other leg?

Accepted Answer

8 units

Answer

4 units

Answer

10 units

Answer

16 units

Question 20

What is the sine of 30 degrees?

Accepted Answer

1/2

Answer

√2/2

Answer

1

Answer

√3/2

Question 21

A ladder leans against a wall, making an angle of 60 degrees with the ground. If the ladder is 12 feet long, how high up the wall does it reach?

Accepted Answer

6√3 feet

Answer

12 feet

Answer

12√3 feet

Answer

6 feet

Question 22

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

Accepted Answer

π

Answer

π/2

Answer

4π

Answer

2π

Question 23

A surveyor measures the angle of elevation to the top of a building as 30 degrees. If the surveyor is standing 100 meters from the base of the building, what is the height of the building?

Accepted Answer

57.74 meters

Answer

100 meters

Answer

173.21 meters

Answer

50 meters

Question 24

What is the value of tan 45 degrees?

Accepted Answer

1

Answer

√3

Answer

√2

Answer

0

Question 25

A triangle has angles of 40 degrees, 60 degrees, and 80 degrees. What type of triangle is it?

Accepted Answer

Scalene triangle

Answer

Isosceles triangle

Answer

Equilateral triangle

Question 26

What is the amplitude of the function y = 3 sin(x)?

Accepted Answer

3

Answer

1

Answer

x

Answer

π

Question 27

Which of the following is NOT a trigonometric function?

Accepted Answer

Logarithmic function

Answer

Cosine function

Answer

Tangent function

Answer

Sine function

Question 28

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

Accepted Answer

5 cm

Answer

2.5 cm

Answer

10 cm

Answer

7.07 cm

Question 29

What is the value of sin(60°)?

Accepted Answer

√3/2

Answer

√2/2

Answer

1

Answer

1/2

Question 30

A surveyor is measuring the height of a building. They stand 100 meters away from the base of the building and measure the angle of elevation to the top of the building as 35 degrees. What is the approximate height of the building?

Accepted Answer

70 meters

Answer

57 meters

Answer

100 meters

Answer

143 meters

Question 31

Which of the following trigonometric identities is TRUE?

Accepted Answer

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

Answer

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

Answer

sin(x) = cos(x) * tan(x)

Answer

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

Question 32

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

Accepted Answer

π

Answer

π/2

Answer

4π

Answer

2π

Question 33

A Ferris wheel has a diameter of 50 meters and takes 10 minutes to complete one rotation. What is the angular velocity of the Ferris wheel in radians per minute?

Accepted Answer

π/5 radians per minute

Answer

π radians per minute

Answer

2π radians per minute

Answer

π/10 radians per minute

Question 34

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

Accepted Answer

A graph that resembles a wave starting at its peak and oscillating between -1 and 1.

Answer

A straight line.

Answer

A graph that resembles a wave starting at its trough and oscillating between -1 and 1.

Question 35

What is the amplitude of the function y = 3sin(x)?

Accepted Answer

3

Answer

π

Answer

2π

Answer

1

Question 36

A ramp is 10 feet long and makes an angle of 15 degrees with the ground. What is the approximate height of the ramp?

Accepted Answer

2.6 feet

Answer

10 feet

Answer

5 feet

Question 37

Which of the following is NOT a solution to the equation sin(x) = 0?

Accepted Answer

π/4

Answer

0

Answer

2π

Answer

π

Question 38

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

Accepted Answer

5 units

Answer

√3 units

Answer

√3/2 units

Answer

10 units

Question 39

What is the value of sin(60°)?

Accepted Answer

√3/2

Answer

1

Answer

1/2

Answer

√2/2

Question 40

A ladder leaning against a wall forms an angle of 60° with the ground. If the ladder is 12 feet long, how high up the wall does the ladder reach?

Accepted Answer

6√3 feet

Answer

6 feet

Answer

12 feet

Answer

12√3 feet

Question 41

Which of the following is NOT a Pythagorean identity?

Accepted Answer

sin²θ + cos²θ = 1/2

Answer

sin²θ + cos²θ = 1

Answer

cot²θ + 1 = csc²θ

Answer

tan²θ + 1 = sec²θ

Question 42

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

Accepted Answer

π

Answer

4π

Answer

π/2

Answer

2π

Question 43

The angle of elevation from a point on the ground to the top of a building is 30 degrees. If the distance from the point to the base of the building is 50 meters, what is the height of the building?

Accepted Answer

50√3/3 meters

Answer

50√3 meters

Answer

25√3 meters

Answer

50 meters

Question 44

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

Accepted Answer

3

Answer

π

Answer

1

Question 45

If sin(θ) = 1/2 and θ is in the first quadrant, what is the value of cos(θ)?

Accepted Answer

√3/2

Answer

1/2

Answer

-1/2

Answer

-√3/2

Question 46

A triangle has sides of length 5, 12, and 13. Is this a right triangle?

Accepted Answer

Yes

Answer

Not enough information

Answer

It's a scalene triangle

Answer

No

Question 47

Which of the following trigonometric functions has a range of all real numbers?

Accepted Answer

y = tan(x)

Answer

y = sin(x)

Answer

y = cot(x)

Answer

y = cos(x)

Question 48

Which of the following is the definition of sine?

Accepted Answer

Ratio of the length of the opposite side to the length of the hypotenuse

Answer

Ratio of the length of the adjacent side to the length of the hypotenuse

Answer

Length of the opposite side

Question 49

What is the value of cos(0)?

Accepted Answer

1

Answer

π/2

Answer

π/4

Answer

0

Question 50

Which of the following identities is true?

Accepted Answer

sin²(x) + cos²(x) = 1

Answer

sin(x) - cos(x) = 1

Answer

sin(x) + cos(x) = 1

Answer

sin²(x) - cos²(x) = 1

Question 51

In a right triangle, what is the relationship between the length of the hypotenuse and the length of the opposite and adjacent sides?

Accepted Answer

Pythagorean Theorem: a² + b² = c²

Answer

Law of Cosines: c² = a² + b² - 2ab cos(C)

Answer

Law of Sines: a/sin(A) = b/sin(B) = c/sin(C)

Answer

None of the above

Question 52

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

Accepted Answer

π

Answer

2π

Answer

π/2

Answer

1

Question 53

Which of the following is an application of trigonometry?

Accepted Answer

Navigation

Answer

Cooking

Answer

Poetry

Answer

None of the above

Question 54

What is the inverse function of sin(x)?

Accepted Answer

arcsin(x)

Answer

cot(x)

Answer

tan(x)

Answer

cos(x)

Question 55

Which of the following is a radian measure?

Accepted Answer

π/3

Answer

30 degrees

Answer

0.5

Answer

180

Question 56

What is the amplitude of the function y = 2sin(x) + 1?

Accepted Answer

2

Answer

0

Answer

1

Answer

-2

Question 57

Which of the following is a unit circle?

Accepted Answer

A circle with radius 1

Answer

A circle with diameter 1

Answer

A circle with circumference 1

Answer

A circle that is tangent to the x- and y-axes