Topic 4 Trigonometry

Question 1

What is the sine of an angle in a right triangle?

Answer 1

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

Question 2

What is the cosine of an angle in a right triangle?

Answer 2

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

Question 3

What is the tangent of an angle in a right triangle?

Answer 3

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

Question 4

True or False: The sine of 90 degrees is 1.

Answer 4

True.

Question 5

What is the value of sin(0 degrees)?

Answer 5

0.

Question 6

What is the value of cos(90 degrees)?

Answer 6

0.

Question 7

Fill in the blank: tan(θ) = ______.

Answer 7

sin(θ) / cos(θ).

Question 8

What is the Pythagorean identity for sine and cosine?

Answer 8

sin²(θ) + cos²(θ) = 1.

Question 9

If sin(θ) = 0.5, what is θ in degrees?

Answer 9

30 degrees or 150 degrees.

Question 10

What is the range of the sine function?

Answer 10

From -1 to 1.

Question 11

What is the range of the cosine function?

Answer 11

From -1 to 1.

Question 12

What is the range of the tangent function?

Answer 12

From negative infinity to positive infinity.

Question 13

True or False: The cosine function is an even function.

Answer 13

True.

Question 14

True or False: The sine function is an odd function.

Answer 14

True.

Question 15

What is the angle in radians equivalent to 180 degrees?

Answer 15

π radians.

Question 16

What is the angle in radians equivalent to 90 degrees?

Answer 16

π/2 radians.

Question 17

What is the sine rule?

Answer 17

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

Question 18

What does the cosine rule state?

Answer 18

c² = a² + b² - 2ab cos(C).

Question 19

Fill in the blank: The unit circle is a circle with a radius of ____.

Answer 19

1.

Question 20

What is the period of the sine function?

Answer 20

2π.

Question 21

What is the period of the cosine function?

Answer 21

2π.

Question 22

What is the period of the tangent function?

Answer 22

π.

Question 23

True or False: The sine and cosine functions are periodic functions.

Answer 23

True.

Question 24

What is the amplitude of the sine function?

Answer 24

1.

Question 25

What is the amplitude of the cosine function?

Answer 25

1.

Question 26

When is the tangent function undefined?

Answer 26

When cos(θ) = 0.

Question 27

What is the value of sin(30 degrees)?

Answer 27

0.5.

Question 28

What is the value of cos(60 degrees)?

Answer 28

0.5.

Question 29

What is the value of tan(45 degrees)?

Answer 29

1.

Question 30

If A + B + C = 180 degrees in a triangle, what does A represent?

Answer 30

An interior angle of the triangle.

Question 31

What is the relationship between the angles of a triangle and their sine values according to the sine rule?

Answer 31

The ratios of the sides are proportional to the sine of their opposite angles.

Question 32

What is the complementary angle of 30 degrees?

Answer 32

60 degrees.

Question 33

What is the complementary angle of 45 degrees?

Answer 33

45 degrees.

Question 34

What is the supplementary angle of 120 degrees?

Answer 34

60 degrees.

Question 35

What is the sine of 45 degrees?

Answer 35

√2 / 2.

Question 36

What is the cosine of 45 degrees?

Answer 36

√2 / 2.

Question 37

True or False: The tangent of an angle is the same in both the first and third quadrants.

Answer 37

True.

Question 38

What is the sine of an angle greater than 90 degrees?

Answer 38

It can be positive or negative, depending on the angle.

Question 39

If sin(θ) = 0.8, what is the range of possible values for θ?

Answer 39

θ could be in the first or second quadrant.

Question 40

What is the value of sin(180 degrees)?

Answer 40

0.

Question 41

What is the value of cos(0 degrees)?

Answer 41

1.