Others

Question 2

What is the definition of a right triangle?

Answer 2

A triangle that has one angle measuring 90 degrees.

Question 3

True or False: The sine of an angle in a right triangle is the ratio of the opposite side to the hypotenuse.

Answer 3

True

Question 4

What is the hypotenuse in a right triangle?

Answer 4

The side opposite the right angle, and the longest side of the triangle.

Question 5

Fill in the blank: The cosine of an angle is the ratio of the ______ side to the hypotenuse.

Answer 5

adjacent

Question 6

What is the Pythagorean theorem?

Answer 6

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

Question 7

What are the primary trigonometric ratios?

Answer 7

Sine, Cosine, and Tangent.

Question 8

True or False: The tangent of an angle is the ratio of the adjacent side to the opposite side.

Answer 8

False

Question 9

What is the formula for sine in a right triangle?

Answer 9

sin(θ) = opposite/hypotenuse

Question 10

What is the formula for cosine in a right triangle?

Answer 10

cos(θ) = adjacent/hypotenuse

Question 11

What is the formula for tangent in a right triangle?

Answer 11

tan(θ) = opposite/adjacent

Question 12

Fill in the blank: The reciprocal of sine is called ______.

Answer 12

cosecant

Question 13

Fill in the blank: The reciprocal of cosine is called ______.

Answer 13

secant

Question 14

Fill in the blank: The reciprocal of tangent is called ______.

Answer 14

cotangent

Question 15

What is the value of sin(90°)?

Answer 15

1

Question 16

What is the value of cos(0°)?

Answer 16

1

Question 17

What is the value of tan(45°)?

Answer 17

1

Question 18

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

Answer 18

True

Question 19

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

Answer 19

True

Question 20

What is the unit circle?

Answer 20

A circle with a radius of 1 centered at the origin of the coordinate plane.

Question 21

What are the coordinates of the point on the unit circle at 0 radians?

Answer 21

(1, 0)

Question 22

What are the coordinates of the point on the unit circle at π/2 radians?

Answer 22

(0, 1)

Question 23

What is the sine of 30 degrees?

Answer 23

1/2

Question 24

What is the cosine of 60 degrees?

Answer 24

1/2

Question 25

What is the tangent of 30 degrees?

Answer 25

√3/3

Question 26

What is the tangent of 60 degrees?

Answer 26

√3

Question 27

Fill in the blank: The angle whose sine is 0 is ______.

Answer 27

0° or 180°

Question 28

Fill in the blank: The angle whose cosine is 0 is ______.

Answer 28

90° or 270°

Question 29

What is the relationship between sine and cosine?

Answer 29

sin(θ) = cos(90° - θ)

Question 30

What is the sine addition formula?

Answer 30

sin(a + b) = sin(a)cos(b) + cos(a)sin(b)

Question 31

What is the cosine addition formula?

Answer 31

cos(a + b) = cos(a)cos(b) - sin(a)sin(b)

Question 32

What is the range of the sine function?

Answer 32

-1 to 1

Question 33

What is the range of the cosine function?

Answer 33

-1 to 1

Question 34

What is the range of the tangent function?

Answer 34

All real numbers

Question 35

What is an angle in standard position?

Answer 35

An angle whose vertex is at the origin and whose initial side lies along the positive x-axis.

Question 36

What is the reference angle?

Answer 36

The acute angle formed by the terminal side of the angle and the x-axis.

Question 37

True or False: The reference angle is always positive.

Answer 37

True

Question 38

What is the relationship between degrees and radians?

Answer 38

180 degrees is equal to π radians.

Question 39

Convert 90 degrees to radians.

Answer 39

π/2 radians

Question 40

Convert 180 degrees to radians.

Answer 40

π radians

Question 41

Convert 360 degrees to radians.

Answer 41

2π radians

Question 42

What is a periodic function?

Answer 42

A function that repeats its values at regular intervals.

Question 43

What is the period of the sine function?

Answer 43

2π

Question 44

What is the period of the cosine function?

Answer 44

2π

Question 45

What is the period of the tangent function?

Answer 45

π

Question 46

What is an amplitude?

Answer 46

The maximum distance from the midline of a wave to its peak.

Question 47

What is the amplitude of the sine function?

Answer 47

1

Question 48

What is the amplitude of the cosine function?

Answer 48

1

Question 49

What is a trigonometric identity?

Answer 49

An equation that is true for all values of the variable.

Question 50

What is the Pythagorean identity?

Answer 50

sin²(θ) + cos²(θ) = 1

Question 51

What is the definition of an angle?

Answer 51

A figure formed by two rays, called the sides of the angle, sharing a common endpoint called the vertex.

Question 52

What is the vertex of an angle?

Answer 52

The common endpoint where the two rays meet.

Question 53

What is a complementary angle?

Answer 53

Two angles that add up to 90 degrees.

Question 54

What is a supplementary angle?

Answer 54

Two angles that add up to 180 degrees.