Trigonometry - Sin, Cos, and Tan

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 length of the adjacent side.

Question 4

True or False: The sine function is periodic.

Answer 4

True

Question 5

What is the Pythagorean identity involving sine and cosine?

Answer 5

sin²(θ) + cos²(θ) = 1

Question 6

Fill in the blank: The angles whose sine is 0 are _____ degrees.

Answer 6

Any integer multiple of 180, e.g., 180 x 1, 180 x 2, 180 x 3… as well as 180 x (-1), 180 x (-2), 180 x (-3)… including 0 = 180 x 0.

Question 7

What is the value of sin(90°)?

Answer 7

1

Question 8

What is the value of cos(0°)?

Answer 8

1

Question 9

What is the value of tan(45°)?

Answer 9

1

Question 10

What is the range of the sine function?

Answer 10

[-1, 1]

Question 11

What is the range of the cosine function?

Answer 11

[-1, 1]

Question 12

True or False: The tangent function can take all real values.

Answer 12

True

Question 13

What is the angle x for which sin(x) = 0.5?

Answer 13

30

Question 14

What is the angle x for which cos(x) = 0.5?

Answer 14

60

Question 15

Fill in the blank: The unit circle has a radius of _____ units.

Answer 15

1

Question 16

What are the coordinates of the point on the unit circle at 90°?

Answer 16

(0, 1)

Question 17

What is the sine value at 180°?

Answer 17

0

Question 18

What is the cosine value at 270°?

Answer 18

0

Question 19

What is the period of the sine and cosine functions?

Answer 19

360° or 2π radians

Question 20

What is the period of the tangent function?

Answer 20

180° or π radians

Question 21

True or False:
sin(θ) = sin(180° - θ).

Answer 21

True