Trigonometry Quizzes: Master Trig Ratios, Identities, and Applications

Question 1

In the trigonometric function **(y = A sin(Bx + C) + D)**, how do amplitude and vertical shift affect the graph?

Accepted Answer

Amplitude controls the vertical stretch or shrink, and vertical shift moves the graph vertically.

Answer

Amplitude and vertical shift affect the horizontal and vertical asymptotes, respectively.

Answer

Amplitude stretches the graph vertically, while vertical shift moves it horizontally.

Answer

Vertical shift affects the vertical asymptotes, while amplitude controls the horizontal movement.

Question 2

The sine of an angle in a right-angled triangle can never be:

Accepted Answer

Greater than 1

Answer

Equal to 0

Answer

Negative

Answer

Greater than 0

Question 3

In surveying, the measurement of the height of a tree utilising the angle of elevation and a known distance involves the application of:

Accepted Answer

Trigonometric ratios

Answer

Pythagoras' theorem

Answer

The law of cosines

Answer

Integration

Question 4

The area of a triangle with a base of 5 cm and a height of 3 cm is:

Accepted Answer

7.5 cm²

Answer

6 cm²

Answer

10 cm²

Answer

15 cm²

Question 5

The law of sines states that in a triangle with sides a, b, and c opposite angles A, B, and C, respectively:

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 6

Which expression represents the cosine of an angle in a right-angled triangle?

Accepted Answer

Adjacent over hypotenuse

Answer

Opposite over hypotenuse

Answer

Hypotenuse over adjacent

Answer

Hypotenuse over opposite

Question 7

Which trigonometric function is undefined at 90°?

Accepted Answer

Tangent

Answer

Sine

Answer

Cosine

Answer

Cosecant

Question 8

A ladder of length 5 meters is leaning against a wall. The base of the ladder is 3 meters from the wall. Calculate the angle between the ladder and the wall (rounded to the nearest degree).

Accepted Answer

53°

Answer

37°

Answer

63°

Answer

78°

Question 9

A ship travels 100 kilometers on a bearing of 030°. It then adjusts its course and sails 50 kilometers on a bearing of 120°. What is the distance between its starting point and final position?

Accepted Answer

150km

Answer

50km

Answer

100km

Answer

200km

Question 10

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

Accepted Answer

2π

Answer

π

Answer

π/2

Answer

4π

Question 11

Which trigonometric function is considered odd?

Accepted Answer

Sine

Answer

Cosine

Answer

Tangent

Answer

Cotangent

Question 12

In a right-angled triangle, the sine of an angle is 0.6. What is the cosine of the same angle?

Accepted Answer

0.8

Answer

0.6

Answer

1.0

Answer

1.2

Question 13

Which of the following trigonometric identities is correct?

Accepted Answer

sin²θ + cos²θ = 1

Answer

tanθ = sinθ - cosθ

Answer

cotθ = tanθ

Answer

cosecθ = cosθ

Question 14

A ladder is leaning against a wall. The base of the ladder is 3m from the wall, and the top of the ladder is 5m high. What is the angle that the ladder makes with the ground?

Accepted Answer

36.9°

Answer

45°

Answer

53.1°

Answer

64.4°

Question 15

In which quadrant is the sine function positive?

Accepted Answer

I and II

Answer

II and III

Answer

III and IV

Answer

IV and I

Question 16

The amplitude of the function y = 2cos(4x - π/2) is:

Accepted Answer

2

Answer

1/2

Answer

1

Answer

4

Question 17

The equation of the midline of the graph of the function y = sinx + 2 is:

Accepted Answer

y = 2

Answer

y = 1

Answer

y = 3

Answer

y = 4

Question 18

Which of the following trigonometric identities can be used to determine the cosine of an angle given its sine?

Accepted Answer

cosθ = ±√(1 - sin²θ)

Answer

sin²θ + cos²θ = 1

Answer

tanθ = sinθ / cosθ

Answer

cotθ = cosθ / sinθ

Question 19

What is the period of the sine function?

Accepted Answer

2π

Answer

π

Answer

1

Answer

½

Question 20

Which of the following is the double-angle formula for cosine?

Accepted Answer

cos(2x) = 2cos²x - 1

Answer

cos(2x) = cos²x - sin²x

Answer

cos(2x) = 1 - 2sin²x

Answer

cos(2x) = sin²x + cos²x

Question 21

What is the value of tan(π/4)?

Accepted Answer

√3

Answer

0

Answer

1

Answer

√2

Question 22

Which of the following is NOT a factor to consider when selecting trigonometry problems for educational purposes?

Accepted Answer

The gender of the students

Answer

The nature of the problem

Answer

The intended learning outcomes

Answer

The age of the students

Question 23

In a right-angled triangle, which of the following is the definition of the cosine of an angle?

Accepted Answer

The ratio of the length of the side adjacent to the angle to the length of the hypotenuse

Answer

The ratio of the length of the side opposite to the angle to the length of the hypotenuse

Answer

The ratio of the length of the side adjacent to the angle to the length of the opposite side

Answer

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

Question 24

What is the value of sin 30°?

Accepted Answer

0.5

Answer

1

Answer

0.75

Answer

0.25

Question 25

Which of the following is the Pythagorean identity?

Accepted Answer

sin²θ + cos²θ = 1

Answer

tan²θ + 1 = sec²θ

Answer

cot²θ - 1 = csc²θ

Answer

sinθ - cosθ = 1

Question 26

What is the period of the function sin 2θ?

Accepted Answer

2π

Answer

π

Answer

π/2

Answer

4π

Question 27

Which of the following trigonometric identities is used to find the value of the third side in a right-angled triangle, given the lengths of the other two sides?

Accepted Answer

Pythagorean theorem

Answer

Sine rule

Answer

Cosine rule

Question 28

Which of the following graphs represents the function y = cos(x) + 1?

Accepted Answer

A cosine wave shifted up by 1 unit

Answer

A sine wave shifted up by 1 unit

Answer

A cosine wave shifted left by 1 unit

Question 29

The angle of elevation from a point on the ground to the top of a building is 45 degrees. If the distance from the point to the base of the building is 20 metres, what is the height of the building?

Accepted Answer

28.28 metres

Answer

20 metres

Answer

40 metres

Question 30

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

Accepted Answer

sin^-1(x)

Answer

cos^-1(x)

Answer

tan^-1(x)

Question 31

Identify which of the listed options is a trigonometric identity:

Accepted Answer

sin² x + cos² x = 1

Answer

tan x = cos x / sin x

Answer

cot x = tan x

Answer

sec x = cos x / tan x

Question 32

A ladder with a length of 5 meters is leaning against a wall. If the bottom of the ladder is 3 meters from the wall, determine the angle between the ladder and the ground.

Accepted Answer

45°

Answer

30°

Answer

60°

Answer

75°

Question 33

Which of the following is the reciprocal of tan x?

Accepted Answer

cot x

Answer

sin x

Answer

cos x

Answer

sec x

Question 34

Calculate the value of sin (π/3). Select the correct answer:

Accepted Answer

√3/2

Answer

0

Answer

1/2

Answer

1

Question 35

Which of the following defines the domain of the trigonometric function tan x?

Accepted Answer

All real numbers except multiples of π/2

Answer

All real numbers

Answer

All real numbers except 0

Answer

All real numbers greater than 0

Question 36

In a right-angled triangle, what is the trigonometric ratio that represents the ratio of the length of the opposite side to the length of the hypotenuse?

Accepted Answer

Sine

Answer

Cosine

Answer

Tangent

Answer

Cosecant

Question 37

Which of the following trigonometric identities is correct?

Accepted Answer

sin²θ + cos²θ = 1

Answer

tanθ = cosθ / sinθ

Answer

cotθ = sinθ / cosθ

Answer

secθ = tanθ / cotθ

Question 38

What is the period of the sine function?

Accepted Answer

2π

Answer

π

Answer

π/2

Answer

2π/3

Question 39

Which transformation shifts the graph of y = sinx to the left by π/2 units?

Accepted Answer

y = sin(x - π/2)

Answer

y = sin(x + π/2)

Answer

y = -sin(x - π/2)

Answer

y = -sin(x + π/2)

Question 40

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

Accepted Answer

2

Answer

1

Answer

3

Answer

6

Question 41

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

Accepted Answer

Sine

Answer

Cosine

Answer

Tangent

Answer

Cotangent

Question 42

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

Accepted Answer

Secant

Answer

Sine

Answer

Cosine

Answer

Cotangent

Question 43

In a right-angled triangle, if the opposite side is 5 cm and the hypotenuse is 13 cm, the length of the adjacent side is:

Accepted Answer

12 cm

Answer

8 cm

Answer

15 cm

Answer

18 cm

Question 44

Which of the following is the unit circle definition of the sine function?

Accepted Answer

The y-coordinate of the point on the unit circle corresponding to the angle.

Answer

The x-coordinate of the point on the unit circle corresponding to the angle.

Answer

The ratio of the length of the opposite side to the length of the hypotenuse in a right-angled triangle.

Answer

The ratio of the length of the adjacent side to the length of the hypotenuse in a right-angled triangle.

Question 45

Which trigonometric identity is represented by the equation sin^2(x) + cos^2(x) = 1?

Accepted Answer

Pythagorean Identity

Answer

Sum-to-Product Identity

Answer

Double-Angle Identity

Answer

Half-Angle Identity

Question 46

Which of the following is the range of sine function?

Accepted Answer

-1 to 1

Answer

-∞ to ∞

Answer

0 to 1

Answer

1 to ∞

Question 47

Select the trigonometric identity that relates sine and cosine:

Accepted Answer

Pythagorean Identity (sin²θ + cos²θ = 1)

Answer

Double Angle Formula (sin2θ = 2sinθcosθ)

Answer

Half Angle Formula (sin(θ/2) = ±√((1 - cosθ)/2))

Answer

Sum and Difference Formula (sin(a+b) = sinacosb + cosa sinb)

Question 48

In a unit circle, determine the value of sin(π/3).

Accepted Answer

√3/2

Answer

0

Answer

1/2

Answer

1

Question 49

Identify the graph that corresponds to the function y = sin(x).

Accepted Answer

A sinusoid

Answer

A straight line

Answer

A circle

Answer

A parabola

Question 50

For the function y = 2cos(3x), determine its period.

Accepted Answer

2π/3

Answer

π/3

Answer

π

Answer

2π

Question 51

Specify the domain of the function y = tan(x).

Accepted Answer

All real numbers except multiples of π/2

Answer

All real numbers

Answer

All real numbers except 0

Answer

All positive real numbers

Question 52

Which of the following is not classified as a trigonometric function?

Accepted Answer

Exponential

Answer

Sine

Answer

Cosine

Answer

Tangent

Question 53

In a right-angled triangle, the trigonometric ratio that represents the length of the side opposite the angle to the length of the hypotenuse is known as:

Accepted Answer

Sine

Answer

Cosine

Answer

Cosecant

Answer

Tangent

Question 54

What is the inverse function of y = cos x?

Accepted Answer

y = arccos x

Answer

y = tan x

Answer

y = sin x

Answer

y = cot x

Question 55

Which of the following equations is a trigonometric identity?

Accepted Answer

sin² x + cos² x = 1

Answer

tan x = sin x / cos x

Answer

cot x = cos x / sin x

Answer

sin x + cos x = 1

Question 56

What is the range of the trigonometric function y = cosec x?

Accepted Answer

All real numbers except 0

Answer

All real numbers including 0

Answer

[-1, 1]

Question 57

Which of the following is the domain of the trigonometric function y = tan x?

Accepted Answer

All real numbers except odd multiples of π/2

Answer

[-π/2, π/2]

Answer

[0, π]

Answer

All real numbers including 0

Question 58

In a right-angled triangle, the sine of an angle is defined as the ratio of which two sides?

Accepted Answer

Opposite side to the Hypotenuse

Answer

Adjacent side to the Opposite side

Answer

Hypotenuse to the Opposite side

Answer

Adjacent side to the Hypotenuse

Question 59

Which trigonometric identity can be used to find the cosine of an angle if the sine and tangent are known?

Accepted Answer

cos²x = 1 - sin²x

Answer

sin²x = tan²x + cos²x

Answer

sin²x + cos²x = 1

Answer

tan²x = sin²x / cos²x

Question 60

What is the distance between two consecutive maximum or minimum points on the graph of a trigonometric function called?

Accepted Answer

Period

Answer

Vertical shift

Answer

Amplitude

Answer

Phase shift

Question 61

What is the inverse function of the sine function?

Accepted Answer

Arcsine

Answer

Cosine

Answer

Tangent

Question 62

In a unit circle, the point (cos(π/3), sin(π/3)) lies in which quadrant?

Accepted Answer

Quadrant I

Answer

Quadrant II

Answer

Quadrant III

Answer

Quadrant IV

Question 63

What is the amplitude of the trigonometric function y = 2sin(3x + π/2)?

Accepted Answer

2

Answer

π/2

Answer

3

Answer

1

Question 64

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

Accepted Answer

Sine

Answer

Tangent

Answer

Cosine

Answer

Cosecant