Deck 5: Trigonometric Functions: Unit Circle Approach

Question 1

Suppose that the terminal point determined by is the point on the unit circle. Find the terminal point determined by
(a) ,
(b) ,
(c) ,
(d) .

Answer 1

(a)
(b)
(c)
(d)

Question 2

Find on the unit circle, given that the - coordinate of is and is in quadrant IV.

Answer 2

is in quadrant IV, so is negative. . So . 

Question 3

Suppose that the terminal point determined by is the point on the unit circle. Find the terminal point determined by
(a) ,
(b) ,
(c) ,
(d) .

Answer 3

(a)
(b)
(c)
(d)

Question 4

On the unit circle, determine which quadrant contains the terminal point of the arc whose length is .

Question 5

Find the reference number and the terminal point determined by .

Question 6

Find the terminal point on the unit circle determined by the value .

Question 7

Suppose that the terminal point determined by is the point . Find the terminal point determined by each of the following:
(a) ,
(b) ,
(c) ,
(d) .

Question 8

Find the reference number and the terminal point determined by .

Question 9

Find the terminal point on the unit circle determined by the value .

Question 10

On the unit circle, determine which quadrant contains the terminal point of the arc whose length is .

Question 11

Find the reference number and the terminal point determined by .

Question 12

Find the terminal point on the unit circle determined by the value .

Question 13

Find on the unit circle, given that the - coordinate of is and is in quadrant III.

Question 14

Find the reference number and the terminal point determined by .

Question 15

Find on the unit circle, given that the - coordinate of is and is in quadrant I.

Question 16

Find the reference number for .

Question 17

Find the exact value of and .

Question 18

Find on the unit circle, given that the - coordinate of is and is in quadrant III.

Question 19

Show that is on the unit circle.

Question 20

Show that is on the unit circle.

Question 21

Find the approximate value of using a calculator.

Question 22

Find the exact value of and .

Question 23

Find the exact value of and .

Question 24

Sketch the graph of .

Question 25

Sketch the graph of .

Question 26

Given that and , find the quadrant in which the terminal point determined by lies.

Question 27

Find the sign of if the terminal point determined by is in quadrant II.

Question 28

Find the exact value of and .

Question 29

If the terminal point determined by is , find , and .

Question 30

Find the exact value of and .

Question 31

Find the values of the trigonometric functions of given that and .

Question 32

If the terminal point determined by is , find , and .

Question 33

Find the values of the trigonometric functions of given that and .

Question 34

Find the approximate value of using a calculator.

Question 35

If the terminal point determined by is , find , and .

Question 36

Find the approximate value of using a calculator.

Question 37

Find the approximate value of using a calculator.

Question 38

Find the exact value of and .

Question 39

Find the sign of if the terminal point determined by is in quadrant IV.

Question 40

Indicate if the function is even, odd or neither.

Question 41

Find the period of the function and sketch its graph.

Question 42

Find the amplitude, period and phase shift of and sketch its graph.

Question 43

Sketch the graph of .

Question 44

Sketch the graph of .

Question 45

Find the period of the function and sketch its graph.

Question 46

Find the amplitude, period and phase shift of and sketch its graph.

Question 47

Find all solutions of the equation that lie in the interval . State each answer correct to two decimal places.

Question 48

Graph the three functions , , and on a common screen. Explain how the graphs are related.

Question 49

Sketch the graph of .

Question 50

Find the amplitude, period, and phase shift of the function , and sketch its graph for one complete period.

Question 51

Find the period of the function and sketch its graph.

Question 52

Graph the three functions , , and on a common screen. Explain how the graphs are related.

Question 53

Find the period of the function and sketch its graph.

Question 54

Find the maximum and minimum values of the function .

Question 55

Sketch the graph of .

Question 56

Find the period of the function and sketch its graph.

Question 57

Find the amplitude, period and phase shift of and sketch its graph.

Question 58

Sketch the graph of .

Question 59

Find the amplitude, period and phase shift of and sketch its graph.

Question 60

Sketch the graph of .

Question 61

Find the exact value of each expression, if it is defined.
(a)
( b)

(c)

Question 62

Find the value of if it is defined.

Question 63

Find the value of if it is defined.

Question 64

Find the value of if it is defined.

Question 65

Find the period of the function and sketch its graph.

Question 66

Find the period of the function and sketch its graph.

Question 67

Find the exact value of each expression, if it is defined.

Question 68

Find the value of if it is defined.

Question 69

Find the period of the function and sketch its graph.

Question 70

Find the period of the function and sketch its graph.

Question 71

Find the period of the function and sketch its graph.

Question 72

Find the value of if it is defined.

Question 73

Find the value of if it is defined.

Question 74

Find the value of if it is defined.

Question 75

Find the period of the function and sketch its graph.

Question 76

Find the period of the function and sketch its graph.

Question 77

Find the approximate value of correct to decimal places.

Question 78

Find the value of if it is defined.

Question 79

Find the value of if it is defined.

Question 80

Find the value of if it is defined.