Basic Trig

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 length of 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 length of 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 sum of the angles in a triangle is always 180 degrees.

Answer 4

True

Question 5

What is the Pythagorean theorem?

Answer 5

In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

Question 6

Fill in the blank: The sine function can be abbreviated as ___.

Answer 6

sin

Question 7

Fill in the blank: The cosine function can be abbreviated as ___.

Answer 7

cos

Question 8

Fill in the blank: The tangent function can be abbreviated as ___.

Answer 8

tan

Question 9

What is the range of the sine function?

Answer 9

The range is from -1 to 1.

Question 10

What is the range of the cosine function?

Answer 10

The range is from -1 to 1.

Question 11

What is the range of the tangent function?

Answer 11

The range is all real numbers.

Question 12

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

Answer 12

True

Question 13

True or False: The cosine of 0 degrees is 0.

Answer 13

False

Question 14

What is the value of tan(45 degrees)?

Answer 14

1

Question 15

What is the relationship between sine and cosine for complementary angles?

Answer 15

sin(θ) = cos(90° - θ)

Question 16

What is the sine law?

Answer 16

In any triangle, the ratio of a side length to the sine of its opposite angle is constant.

Question 17

What is the cosine law?

Answer 17

c² = a² + b² - 2ab * cos(C), where c is the side opposite angle C.

Question 18

What are the coordinates of the unit circle at 0 degrees?

Answer 18

(1, 0)

Question 19

What is the value of sin(30 degrees)?

Answer 19

0.5

Question 20

What is the value of cos(60 degrees)?

Answer 20

0.5

Question 21

What is the value of tan(30 degrees)?

Answer 21

√3/3

Question 22

What is the period of the sine function?

Answer 22

360 degrees or 2π radians.

Question 23

What is the period of the cosine function?

Answer 23

360 degrees or 2π radians.

Question 24

What is the period of the tangent function?

Answer 24

180 degrees or π radians.