Graphs of trigonometric functions

Question 1

For an angle θ in a right angled triangle, what is sin(θ) equal to?

Answer 1

opposite/hypotenuse

Question 2

For an angle θ in a right angled triangle, what is cos(θ) equal to?

Answer 2

adjacent/hypotenuse

Question 3

For an angle θ in a right angled triangle, what is tan(θ) equal to?

Answer 3

opposite/adjacent

Question 4

What convention is used when referring to angles in an x–y plane?

Answer 4

It goes anticlockwise, measured from the positive x axis

Question 5

Which out of sin(θ), cos(θ) and tan(θ) are positive in the first quadrant?

Answer 5

All of them

Question 6

Which out of sin(θ), cos(θ) and tan(θ) are positive in the second quadrant?

Answer 6

sin(θ)

Question 7

Which out of sin(θ), cos(θ) and tan(θ) are positive in the third quadrant?

Answer 7

tan(θ)

Question 8

Which out of sin(θ), cos(θ) and tan(θ) are positive in the fourth quadrant?

Answer 8

cos(θ)

Question 9

What is sin(180°-θ) equal to?

Answer 9

sin(θ)

Question 10

What is sin(180°+θ) equal to?

Answer 10

-sin(θ)

Question 11

What is sin(360°-θ) equal to?

Answer 11

-sin(θ)

Question 12

What is cos(180°-θ) equal to?

Answer 12

-cos(θ)

Question 13

What is cos(180°+θ) equal to?

Answer 13

-cos(θ)

Question 14

What is cos(360°-θ) equal to?

Answer 14

cos(θ)

Question 15

What is tan(180°-θ) equal to?

Answer 15

-tan(θ)

Question 16

What is tan(180°+θ) equal to?

Answer 16

tan(θ)

Question 17

What is tan(360°-θ) equal to?

Answer 17

-tan(θ)

Question 18

What is sin(0°)?

Answer 18

0

Question 19

What is sin(30°)?

Answer 19

0.5

Question 20

What is sin(45°)?

Answer 20

√(2)/2

Question 21

What is sin(60°)?

Answer 21

√(3)/2

Question 22

What is sin(90°)?

Answer 22

1

Question 23

What is cos(0°)?

Answer 23

1

Question 24

What is cos(30°)?

Answer 24

√(3)/2

Question 25

What is cos(45°)?

Answer 25

√(2)/2

Question 26

What is cos(60°)?

Answer 26

0.5

Question 27

What is cos(90°)?

Answer 27

0

Question 28

What is tan(0°)?

Answer 28

0

Question 29

What is tan(30°)?

Answer 29

√(3)/3

Question 30

What is tan(45°)?

Answer 30

1

Question 31

What is tan(60°)?

Answer 31

√(3)

Question 32

What is tan(90°)?

Answer 32

Undefined

Question 33

What is sin(θ+360°) equal to?

Answer 33

sin(θ)

Question 34

What is sin(θ-360°) equal to?

Answer 34

sin(θ)

Question 35

What is sin(90°-θ)-sin(90°+θ) equal to?

Answer 35

0

Question 36

What is cos(θ+360°) equal to?

Answer 36

cos(θ)

Question 37

What is cos(θ-360°) equal to?

Answer 37

cos(θ)

Question 38

What is cos(-θ)-cos(θ) equal to?

Answer 38

0

Question 39

What is tan(θ+180°) equal to?

Answer 39

tan(θ)

Question 40

What is tan(θ-180°) equal to?

Answer 40

tan(θ)

Question 41

What does the graph of y=f(x+a) where a is a constant look like, compared to the graph of y=f(x)?

Answer 41

It has been horizontally translated by -a

Question 42

What does the graph of y=f(x)+a where a is a constant look like, compared to the graph of y=f(x)?

Answer 42

It has been vertically translated by a

Question 43

What does the graph of y=f(ax) where a is a constant look like, compared to the graph of y=f(x)?

Answer 43

It has been horizontally stretched by a scale factor of 1/a

Question 44

What does the graph of y=af(x) where a is a constant look like, compared to the graph of y=f(x)?

Answer 44

It has been vertically stretched by a scale factor of a

Question 45

What is sin(-θ) equal to?

Answer 45

-sin(θ)

Question 46

What is cos(-θ) equal to?

Answer 46

cos(θ)

Question 47

What is tan(-θ) equal to?

Answer 47

-tan(θ)

Question 48

What is sin(90°-θ) equal to?

Answer 48

cos(θ)

Question 49

What is cos(90°-θ) equal to?

Answer 49

sin(θ)