Trigonometry

Question 1

It is a branch of mathematics that focuses on relationships between the sides and angles of triangles.

Answer 1

Trigonometry

Question 2

These are formed by an initial side and a terminal side.

Answer 2

Angles

Question 3

If the angle is made by a rotation in the counterclockwise direction, what type of angle will it create?

Answer 3

A Positive angle

Question 4

Convert 275° to radian.

Answer 4

55π/36 rad

Question 5

Convert 3𝜋/2 radian into degrees

Answer 5

270°

Question 6

Convert -7𝜋/3 radian into degrees

Answer 6

-420°

Question 7

Convert 75° into radians.

Answer 7

5𝜋/12

Question 8

These are angles in standard position with terminal sides that lie along the x or y-axis.

Answer 8

Quadrantal Angles

Question 9

These are 2 different angles with the same initial and terminal sides.

Answer 9

Co-terminal Angles

Question 10

[DMS - Degrees] 38°41’42“

Answer 10

38.692°

Question 11

[DMS - Degrees] 72°54’32“

Answer 11

72.90889°

Question 12

[DMS - Degrees] 13°61’76“

Answer 12

14.0377°

Question 13

[Degrees- DMS] 128.77°

Answer 13

128°46’12“

Question 14

[Degrees- DMS] 37.425°

Answer 14

37°25’30“

Question 15

Give the positive co-terminal angle of -442°

Answer 15

278°

Question 16

Give the negative co-terminal angle of -442°

Answer 16

-82°

Question 17

[Identifying Quadrant] 220°

Answer 17

Quadrant III

Question 18

[Identifying Quadrant] -620°

Answer 18

Quadrant II

Question 19

[Identifying Quadrant] 68°

Answer 19

Quadrant I

Question 20

[Identifying Quadrant] 5𝜋/4°

Answer 20

Quadrant III

Question 21

[Identifying Quadrant] 32𝜋/5°

Answer 21

Quadrant I

Question 22

[Identifying Quadrant] -5𝜋/3°

Answer 22

Quadrant IV

Question 23

Find the area of the sector whose radius and central angle are 42 cm and
60° respectively.

Answer 23

294π cm^2

Question 24

Peter and his partner are conducting a physics experiment on pendulum motion. Their 30 cm pendulum traverses an arc of 15 cm. To
the nearest degree, how many degrees of rotation did the pendulum swing?

Answer 24

28.65°

Question 25

Ashley has a sprinkler that has several varieties of coverage. The quarter-circle sprinkler head sprays water a distance of up to 20 feet from the head. What area will be covered by the spray of the quarter-circle sprinkler head? Round your answer to three decimal places.

Answer 25

314.1516 ft^2

Question 26

Ashley has a sprinkler that has several varieties of coverage. The quarter-circle sprinkler head sprays water a distance of up to 20 feet from the head. What area will be covered by the spray of the quarter-circle sprinkler head? Round your answer to three decimal places.

Answer 26

314.1516 ft^2

Question 27

What is the cotθ of P(3,5)?

Answer 27

3/5

Question 28

What is the tanθ of P(1,-4)?

Answer 28

-4

Question 29

[Identify Quadrant] tanθ > 0, secθ <0

Answer 29

Quadrant III

Question 30

[Identify Quadrant] cosθ > 0, sinθ >0

Answer 30

Quadrant I

Question 31

If sinθ = √3/2 and tanθ > 0, find the value of the adjacent side (x).

Answer 31

x = 1

Question 32

If cscθ = √2 and cosθ > 0, find the value of the cosθ.

Answer 32

cscθ = √2/2

Question 33

If cscθ = √2 and cosθ > 0, find the value of the cosθ.

Answer 33

cscθ = √2/2

Question 34

These are positive acute angles (between 0 to 90 degrees) formed by the terminal side and x-axis.

Answer 34

Reference Angles

Question 35

Find the reference angle of 240°

Answer 35

60°

Question 36

Find the reference angle of -165°

Answer 36

15°

Question 37

Find the reference angle of 11𝜋/2

Answer 37

𝜋/2

Question 38

What is tan(7𝜋/4)?

Answer 38

1

Question 39

What is cos(390°)?

Answer 39

√3/2

Question 40

What is the range for cotθ and tanθ?

Answer 40

All real numbers (-∞, ∞)

Question 41

It is how far the function is shifted horizontally from the usual position.

Answer 41

Phase shift

Question 42

What value of would make the function undefined?