Trigonometric Functions: Master the Basics for Nursing Students

Question 1

Which of the following is the graph of the function y = 2sin(x - π/4)?

Accepted Answer

A graph of the sine function shifted π/4 units to the right

Answer

A graph of the sine function shifted π/4 units to the left

Answer

A graph of the cosine function shifted π/4 units to the left

Answer

A graph of the cosine function shifted π/4 units to the right

Question 2

What is the value of cos(π/3)?

Accepted Answer

√3/2

Answer

1/2

Answer

1

Answer

0

Question 3

Which of the following identities is used to find the sine of the sum of two angles?

Accepted Answer

sin(x + y) = sin(x) + sin(y)

Answer

cos(x + y) = cos(x) + cos(y)

Answer

tan(x + y) = tan(x) + tan(y)

Answer

cot(x + y) = cot(x) + cot(y)

Question 4

What is the inverse function of the tangent function?

Accepted Answer

arctan(x)

Answer

sin(x)

Answer

cos(x)

Answer

tan(x)

Question 5

Which of the following is the equation of the graph that passes through the points (0, 3) and (π, 0)?

Accepted Answer

y = 3sin(x)

Answer

y = 3cos(x)

Answer

y = -3cos(x)

Answer

y = -3sin(x)

Question 6

What is the sum of the interior angles of a triangle?

Accepted Answer

180 degrees

Answer

a + b + c

Answer

π radians

Answer

90 degrees

Question 7

Which trigonometric function is used to find the height of an object based on its angle of elevation and distance from the observer?

Accepted Answer

Tangent

Answer

Sine

Answer

Cosine

Answer

Cotangent

Question 8

Which of the following choices defines the period of the sine function?

Accepted Answer

2π

Answer

π

Answer

π/2

Answer

3π/2

Question 9

Given that the sine of angle θ equals 0.5, what is the measure of angle θ?

Accepted Answer

30°

Answer

45°

Answer

60°

Answer

90°

Question 10

Which trigonometric function represents the ratio of the opposite side to the adjacent side in a right triangle?

Accepted Answer

Tangent

Answer

Sine

Answer

Cosine

Answer

Cotangent

Question 11

What is the range of possible values for the cosine function?

Accepted Answer

[-1, 1]

Answer

[0, 1]

Answer

[-∞, ∞]

Answer

[0, ∞)

Question 12

A nurse wants to calculate the height of a building by measuring the angle of elevation of the sun. Which trigonometric function should she use in her calculations?

Accepted Answer

Tangent

Answer

Sine

Answer

Cosine

Answer

Cotangent

Question 13

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

Accepted Answer

3

Answer

1

Answer

2

Answer

-3

Question 14

Which of the following equations represents the inverse cosine function?

Accepted Answer

y = cos⁻¹(x)

Answer

y = arccos(x)

Answer

y = sin(arccos(x))

Answer

y = 1/cos(x)

Question 15

What is the range of the sine function?

Accepted Answer

[-1, 1]

Answer

[-∞, ∞]

Answer

[0, 1]

Answer

[1, ∞]

Question 16

Which trigonometric identity is used to find the cosine of a sum of angles?

Accepted Answer

cos(α ± β) = cosα cosβ ∓ sinα sinβ

Answer

sin(α ± β) = sinα cosβ ± cosα sinβ

Answer

tan(α ± β) = tanα ± tanβ

Answer

cot(α ± β) = cotα cotβ ± 1

Question 17

What is the inverse function of the sine function?

Accepted Answer

Arcsine

Answer

Cosine

Answer

Tangent

Answer

Arctangent

Question 18

To calculate a building's height using trigonometry, a nurse needs to find the angle of elevation to the sun. Which inverse trigonometric function should the nurse use?

Accepted Answer

arccosine

Answer

arcsine

Answer

arctangent

Answer

arccotangent

Question 19

Which of the following accurately defines the sine function?

Accepted Answer

The ratio of the opposite side's length to the hypotenuse's length

Answer

The ratio of the adjacent side's length to the hypotenuse's length

Answer

The ratio of the opposite side's length to the adjacent side's length

Answer

The sum of the adjacent and opposite sides' lengths

Question 20

What is the period of the cosine function?

Accepted Answer

2π

Answer

π/2

Answer

π

Answer

4π

Question 21

Identify the amplitude of the function y = 2cos(3x).

Accepted Answer

2

Answer

1

Answer

3

Answer

4

Question 22

In a right triangle with a hypotenuse of 10 cm and an angle of 30 degrees, find the length of the opposite side.

Accepted Answer

5√3 cm

Answer

5 cm

Answer

10 cm

Answer

10√3 cm

Question 23

Which function is the inverse of cosine?

Accepted Answer

arccos

Answer

arcsin

Answer

arctan

Answer

arccot

Question 24

What is the range of the tangent function?

Accepted Answer

(-∞, -1] ∪ [1, ∞)

Answer

(-1, 1)

Answer

[0, 1)

Answer

(0, ∞)

Question 25

Which graph accurately represents the function y = tan(x + π/4)?

Accepted Answer

A graph of the tangent function shifted π/4 units to the right

Answer

A graph of the tangent function shifted π/4 units to the left

Answer

A graph of the tangent function shifted π/2 units to the right

Answer

A graph of the tangent function shifted π/2 units to the left

Question 26

For the function f(x) = sin(2x), identify its period.

Accepted Answer

2π

Answer

π

Answer

4π

Answer

8π

Question 27

Determine the amplitude of the function f(x) = -2cos(x).

Accepted Answer

2

Answer

1

Answer

3

Answer

4

Question 28

Which of the following expressions is equivalent to the definition of tangent (tan(θ))?

Accepted Answer

sin(θ) / cos(θ)

Answer

cos(θ) / sin(θ)

Answer

1 / sin(θ)

Answer

1 / cos(θ)

Question 29

Solve the equation 2sin(x) - 1 = 0 within the interval [0, 2π).

Accepted Answer

x = π/3, 2π/3

Answer

x = π/6, 5π/6

Answer

x = π/4, 3π/4

Answer

x = 0, 2π

Question 30

Identify the inverse function of f(x) = tan(x).

Accepted Answer

y = arctan(x)

Answer

y = sin(x)

Answer

y = cos(x)

Answer

y = cot(x)

Question 31

Using trigonometric identities, calculate the value of sin(π/6) + cos(π/6).

Accepted Answer

√3/2

Answer

0

Answer

1

Answer

√2/2

Question 32

A nurse needs to determine the angle of depression to a patient lying in bed. Which trigonometric function should they use and why?

Accepted Answer

Sine

Answer

Cosine

Answer

Tangent

Answer

Secant

Question 33

Define the sine function. Which of the following represents the ratio of the length of the opposite side to the length of the hypotenuse of a right triangle?

Accepted Answer

sin(θ) = opposite/hypotenuse

Answer

tan(θ) = opposite/adjacent

Answer

cos(θ) = adjacent/hypotenuse

Question 34

Calculate the value of sin(π/2). Which of the following is correct?

Accepted Answer

1

Answer

-1

Answer

0

Answer

π/2

Question 35

Identify the period of the cosine function. Which of the following represents the distance between two consecutive peaks or troughs of the cosine curve?

Accepted Answer

2π

Answer

π/2

Answer

4π

Answer

π

Question 36

Determine the amplitude of the function y = 2cos(3x + π/4). Which of the following represents half the distance between the maximum and minimum values of the function?

Accepted Answer

2

Answer

3

Answer

π/4

Answer

1

Question 37

Identify the inverse function of the cosine function. Which of the following represents the function that undoes the cosine operation?

Accepted Answer

arccos

Answer

arcsin

Answer

acos

Answer

arctan

Question 38

Which of the following is NOT a trigonometric function?

Accepted Answer

Logarithm

Answer

Tangent

Answer

Cosine

Answer

Sine

Question 39

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

Accepted Answer

π

Answer

π/2

Answer

4π

Answer

2π

Question 40

The angle of elevation from a point on the ground to the top of a building is 60°. 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 meters

Answer

25√3 meters

Answer

100 meters

Answer

50 meters

Question 41

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

Accepted Answer

3

Answer

2π

Answer

π

Answer

1