Unit Circle Flashcards: 16 Angles, Radians & Exact Coordinates

Question 1

Convert 0° to radians in [0, 2π).

Accepted Answer

0

Question 2

Convert 30° to radians in [0, 2π).

Accepted Answer

π/6

Question 3

Convert 45° to radians in [0, 2π).

Accepted Answer

π/4

Question 4

Convert 60° to radians in [0, 2π).

Accepted Answer

π/3

Question 5

Convert 90° to radians in [0, 2π).

Accepted Answer

π/2

Question 6

Convert 120° to radians in [0, 2π).

Accepted Answer

2π/3

Question 7

Convert 135° to radians in [0, 2π).

Accepted Answer

3π/4

Question 8

Convert 150° to radians in [0, 2π).

Accepted Answer

5π/6

Question 9

Convert 180° to radians in [0, 2π).

Accepted Answer

π

Question 10

Convert 210° to radians in [0, 2π).

Accepted Answer

7π/6

Question 11

Convert 225° to radians in [0, 2π).

Accepted Answer

5π/4

Question 12

Convert 240° to radians in [0, 2π).

Accepted Answer

4π/3

Question 13

Convert 270° to radians in [0, 2π).

Accepted Answer

3π/2

Question 14

Convert 300° to radians in [0, 2π).

Accepted Answer

5π/3

Question 15

Convert 315° to radians in [0, 2π).

Accepted Answer

7π/4

Question 16

Convert 330° to radians in [0, 2π).

Accepted Answer

11π/6

Question 17

For the unit-circle position 30° = π/6, give the exact ordered pair (cos θ, sin θ).

Accepted Answer

(√3/2, 1/2)

Question 18

For the unit-circle position 225° = 5π/4, give the exact ordered pair (cos θ, sin θ).

Accepted Answer

(−√2/2, −√2/2)

Question 19

For the unit-circle position 120° = 2π/3, give the exact ordered pair (cos θ, sin θ).

Accepted Answer

(−1/2, √3/2)

Question 20

For the unit-circle position 270° = 3π/2, give the exact ordered pair (cos θ, sin θ).

Accepted Answer

(0, −1)

Question 21

For the unit-circle position 150° = 5π/6, give the exact ordered pair (cos θ, sin θ).

Accepted Answer

(−√3/2, 1/2)

Question 22

For the unit-circle position 315° = 7π/4, give the exact ordered pair (cos θ, sin θ).

Accepted Answer

(√2/2, −√2/2)

Question 23

For the unit-circle position 240° = 4π/3, give the exact ordered pair (cos θ, sin θ).

Accepted Answer

(−1/2, −√3/2)

Question 24

For the unit-circle position 0° = 0, give the exact ordered pair (cos θ, sin θ).

Accepted Answer

(1, 0)

Question 25

For the unit-circle position 210° = 7π/6, give the exact ordered pair (cos θ, sin θ).

Accepted Answer

(−√3/2, −1/2)

Question 26

For the unit-circle position 45° = π/4, give the exact ordered pair (cos θ, sin θ).

Accepted Answer

(√2/2, √2/2)

Question 27

For the unit-circle position 300° = 5π/3, give the exact ordered pair (cos θ, sin θ).

Accepted Answer

(1/2, −√3/2)

Question 28

For the unit-circle position 90° = π/2, give the exact ordered pair (cos θ, sin θ).

Accepted Answer

(0, 1)

Question 29

For the unit-circle position 330° = 11π/6, give the exact ordered pair (cos θ, sin θ).

Accepted Answer

(√3/2, −1/2)

Question 30

For the unit-circle position 135° = 3π/4, give the exact ordered pair (cos θ, sin θ).

Accepted Answer

(−√2/2, √2/2)

Question 31

For the unit-circle position 60° = π/3, give the exact ordered pair (cos θ, sin θ).

Accepted Answer

(1/2, √3/2)

Question 32

For the unit-circle position 180° = π, give the exact ordered pair (cos θ, sin θ).

Accepted Answer

(−1, 0)

Question 33

Convert π/2 radians to degrees in [0°, 360°).

Accepted Answer

90°

Question 34

Convert 7π/6 radians to degrees in [0°, 360°).

Accepted Answer

210°

Question 35

Convert π/4 radians to degrees in [0°, 360°).

Accepted Answer

45°

Question 36

Convert 2π/3 radians to degrees in [0°, 360°).

Accepted Answer

120°

Question 37

Convert 3π/2 radians to degrees in [0°, 360°).

Accepted Answer

270°

Question 38

Convert π/6 radians to degrees in [0°, 360°).

Accepted Answer

30°

Question 39

Convert 5π/4 radians to degrees in [0°, 360°).

Accepted Answer

225°

Question 40

Convert 5π/3 radians to degrees in [0°, 360°).

Accepted Answer

300°

Question 41

Convert 0 radians to degrees in [0°, 360°).

Accepted Answer

0°

Question 42

Convert 5π/6 radians to degrees in [0°, 360°).

Accepted Answer

150°

Question 43

Convert 7π/4 radians to degrees in [0°, 360°).

Accepted Answer

315°

Question 44

Convert π/3 radians to degrees in [0°, 360°).

Accepted Answer

60°

Question 45

Convert π radians to degrees in [0°, 360°).

Accepted Answer

180°

Question 46

Convert 11π/6 radians to degrees in [0°, 360°).

Accepted Answer

330°

Question 47

Convert 3π/4 radians to degrees in [0°, 360°).

Accepted Answer

135°

Question 48

Convert 4π/3 radians to degrees in [0°, 360°).

Accepted Answer

240°

Question 49

In [0, 2π), which unit-circle angle has exact coordinates (cos θ, sin θ) = (−1, 0)?

Accepted Answer

π

Equivalent degree measure: 180°.

Question 50

In [0, 2π), which unit-circle angle has exact coordinates (cos θ, sin θ) = (√3/2, 1/2)?

Accepted Answer

π/6

Equivalent degree measure: 30°.

Question 51

In [0, 2π), which unit-circle angle has exact coordinates (cos θ, sin θ) = (√2/2, −√2/2)?

Accepted Answer

7π/4

Equivalent degree measure: 315°.

Question 52

In [0, 2π), which unit-circle angle has exact coordinates (cos θ, sin θ) = (−1/2, √3/2)?

Accepted Answer

2π/3

Equivalent degree measure: 120°.

Question 53

In [0, 2π), which unit-circle angle has exact coordinates (cos θ, sin θ) = (1, 0)?

Accepted Answer

0

Equivalent degree measure: 0°.

Question 54

In [0, 2π), which unit-circle angle has exact coordinates (cos θ, sin θ) = (−√3/2, −1/2)?

Accepted Answer

7π/6

Equivalent degree measure: 210°.

Question 55

In [0, 2π), which unit-circle angle has exact coordinates (cos θ, sin θ) = (−√2/2, √2/2)?

Accepted Answer

3π/4

Equivalent degree measure: 135°.

Question 56

In [0, 2π), which unit-circle angle has exact coordinates (cos θ, sin θ) = (1/2, −√3/2)?

Accepted Answer

5π/3

Equivalent degree measure: 300°.

Question 57

In [0, 2π), which unit-circle angle has exact coordinates (cos θ, sin θ) = (0, −1)?

Accepted Answer

3π/2

Equivalent degree measure: 270°.

Question 58

In [0, 2π), which unit-circle angle has exact coordinates (cos θ, sin θ) = (−√3/2, 1/2)?

Accepted Answer

5π/6

Equivalent degree measure: 150°.

Question 59

In [0, 2π), which unit-circle angle has exact coordinates (cos θ, sin θ) = (√2/2, √2/2)?

Accepted Answer

π/4

Equivalent degree measure: 45°.

Question 60

In [0, 2π), which unit-circle angle has exact coordinates (cos θ, sin θ) = (−1/2, −√3/2)?

Accepted Answer

4π/3

Equivalent degree measure: 240°.

Question 61

In [0, 2π), which unit-circle angle has exact coordinates (cos θ, sin θ) = (0, 1)?

Accepted Answer

π/2

Equivalent degree measure: 90°.

Question 62

In [0, 2π), which unit-circle angle has exact coordinates (cos θ, sin θ) = (√3/2, −1/2)?

Accepted Answer

11π/6

Equivalent degree measure: 330°.

Question 63

In [0, 2π), which unit-circle angle has exact coordinates (cos θ, sin θ) = (−√2/2, −√2/2)?

Accepted Answer

5π/4

Equivalent degree measure: 225°.

Question 64

In [0, 2π), which unit-circle angle has exact coordinates (cos θ, sin θ) = (1/2, √3/2)?

Accepted Answer

π/3

Equivalent degree measure: 60°.

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Unit Circle Flashcards

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Unit Circle Flashcards: 16 Angles, Radians & Exact Coordinates