Trigonometry

Question 1

What is the Pythagorean theorem?

Answer 1

In a right triangle, a² + b² = c², where c is the hypotenuse.

Question 2

What are the primary trigonometric ratios?

Answer 2

Sine, Cosine, and Tangent.

Question 3

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

Answer 3

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

Question 4

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

Answer 4

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

Question 5

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

Answer 5

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

Question 6

True or False: The sine function is defined for all angles.

Answer 6

True.

Question 7

Fill in the blank: In a right triangle, tan(θ) = _____.

Answer 7

opposite/adjacent.

Question 8

What is the range of the sine function?

Answer 8

[-1, 1].

Question 9

What is the range of the cosine function?

Answer 9

[-1, 1].

Question 10

What is the range of the tangent function?

Answer 10

All real numbers.

Question 11

What is the formula for finding the hypotenuse using sine?

Answer 11

hypotenuse = opposite/sine(θ).

Question 12

What is the formula for finding the opposite side using cosine?

Answer 12

opposite = hypotenuse * sine(θ).

Question 13

What is the cosine of 0 degrees?

Answer 13

1.

Question 14

What is the sine of 90 degrees?

Answer 14

1.

Question 15

What is the value of tan(45 degrees)?

Answer 15

1.

Question 16

What does SOHCAHTOA stand for?

Answer 16

Sine = Opposite/Hypotenuse, Cosine = Adjacent/Hypotenuse, Tangent = Opposite/Adjacent.

Question 17

If sin(θ) = 1/2, what is θ in degrees?

Answer 17

30 degrees or 150 degrees.

Question 18

If cos(θ) = 0, what are the possible angles for θ?

Answer 18

90 degrees or 270 degrees.

Question 19

How do you convert radians to degrees?

Answer 19

Multiply by 180/π.

Question 20

What is the value of sin(180 degrees)?

Answer 20

0.

Question 21

What is the value of cos(180 degrees)?

Answer 21

-1.

Question 22

What is the sine rule?

Answer 22

a/sin(A) = b/sin(B) = c/sin(C), where a, b, c are sides and A, B, C are opposite angles.

Question 23

What is the cosine rule?

Answer 23

c² = a² + b² - 2ab*cos(C).

Question 24

True or False: The sine function is periodic.

Answer 24

True.

Question 25

What is the period of the sine function?

Answer 25

360 degrees or 2π radians.

Question 26

What is the period of the cosine function?

Answer 26

360 degrees or 2π radians.

Question 27

What is the period of the tangent function?

Answer 27

180 degrees or π radians.

Question 28

What is the reference angle for 210 degrees?

Answer 28

30 degrees.

Question 29

What is the reference angle for 330 degrees?

Answer 29

30 degrees.

Question 30

True or False: The tangent function is undefined at 90 degrees.

Answer 30

True.

Question 31

What is the value of sin(270 degrees)?

Answer 31

-1.

Question 32

If tan(θ) = 0, what is θ?

Answer 32

0 degrees, 180 degrees, or any multiple of 180 degrees.

Question 33

What is the value of cos(90 degrees)?

Answer 33

0.

Question 34

What is the value of sin(360 degrees)?

Answer 34

0.

Question 35

Fill in the blank: The opposite side is opposite to the _____.

Answer 35

angle.

Question 36

What is the hypotenuse in a 3-4-5 triangle?

Answer 36

5.

Question 37

What is the length of the adjacent side in a triangle with an angle of 30 degrees and hypotenuse of 10?

Answer 37

√3 * 5 (approximately 8.66).

Question 38

If sin(θ) = 0.5, what is the value of θ in radians?

Answer 38

π/6 or 5π/6.

Question 39

What is the tangent of 30 degrees?

Answer 39

1/√3 or √3/3.

Question 40

What is the cosine of 45 degrees?

Answer 40

√2/2.

Question 41

What quadrant is sin positive and cos negative?

Answer 41

Quadrant II.

Question 42

What quadrant is tan positive?

Answer 42

Quadrant I and III.

Question 43

What is the sine of 60 degrees?

Answer 43

√3/2.

Question 44

What is the cosine of 30 degrees?

Answer 44

√3/2.

Question 45

What is the tangent of 60 degrees?

Answer 45

√3.

Question 46

Fill in the blank: The law of sines can be used in non-right triangles using the formula _____.

Answer 46

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

Question 47

Fill in the blank: The law of cosines is used to find a side when you know _____.

Answer 47

two sides and the included angle.

Question 48

True or False: The sum of angles in a triangle is always 180 degrees.

Answer 48

True.

Question 49

What is the formula for finding the area of a triangle using sine?

Answer 49

Area = 1/2 * a * b * sin(C).

Question 50

What is the value of sin(45 degrees)?

Answer 50

√2/2.

Question 51

What is the length of the opposite side in a triangle with an angle of 60 degrees and hypotenuse of 8?

Answer 51

4√3 (approximately 6.93).

Question 52

What is the value of cos(0 degrees)?

Answer 52

1.

Question 53

What is the value of tan(0 degrees)?

Answer 53

0.

Question 54

What is the complementary angle of 30 degrees?

Answer 54

60 degrees.

Question 55

What is the complementary angle of 45 degrees?

Answer 55

45 degrees.

Question 56

What is the complementary angle of 60 degrees?

Answer 56

30 degrees.

Question 57

What is the exact value of sin(30 degrees)?

Answer 57

1/2.

Question 58

What is the exact value of cos(60 degrees)?

Answer 58

1/2.

Question 59

What is the exact value of tan(30 degrees)?

Answer 59

1/√3.

Question 60

What does it mean for two angles to be co-terminal?

Answer 60

They differ by a multiple of 360 degrees or 2π radians.

Question 61

What is the sine of an angle in the fourth quadrant?

Answer 61

Negative.

Question 62

What is the cosine of an angle in the second quadrant?

Answer 62

Negative.

Question 63

Fill in the blank: The sine of an angle is the same as the cosine of its _____.

Answer 63

complement.

Question 64

What is the angle of elevation?

Answer 64

The angle formed by the line of sight above the horizontal.

Question 65

What is the angle of depression?

Answer 65

The angle formed by the line of sight below the horizontal.

Question 66

What is the relationship between the sides in a 45-45-90 triangle?

Answer 66

The legs are equal, and the hypotenuse is √2 times a leg.

Question 67

What is the relationship between the sides in a 30-60-90 triangle?

Answer 67

The lengths are in the ratio 1:√3:2.

Question 68

What is the sine of 120 degrees?

Answer 68

√3/2.

Question 69

What is the cosine of 120 degrees?

Answer 69

-1/2.

Question 70

What is the tangent of 120 degrees?

Answer 70

-√3.

Question 71

True or False: The unit circle is used to define trigonometric functions.

Answer 71

True.

Question 72

Fill in the blank: The coordinates of a point on the unit circle can be expressed as (_____, _____).

Answer 72

cos(θ), sin(θ).

Question 73

What is the value of sin(π)?

Answer 73

0.

Question 74

What is the value of cos(π)?

Answer 74

-1.

Question 75

What is the value of tan(π/4)?

Answer 75

1.

Question 76

What is the formula for converting degrees to radians?

Answer 76

Multiply by π/180.

Question 77

What is the value of sin(1 radian) approximately?

Answer 77

0.84.

Question 78

What is the value of cos(1 radian) approximately?

Answer 78

0.54.

Question 79

What is the value of tan(1 radian) approximately?

Answer 79

1.56.

Question 80

What is the relationship between degrees and radians?

Answer 80

180 degrees = π radians.

Question 81

What is the value of sin(2π)?

Answer 81

0.

Question 82

What is the value of cos(2π)?

Answer 82

1.