Circular functions

Question 1

State the rule for the function

Answer 1

Question 2

quick sketch

Answer 2

Question 3

Answer 3

Question 4

State the rule for the function

Answer 4

Question 5

quick sketch

Answer 5

Question 6

State the rule for the function

Answer 6

Question 7

Answer 7

State the rule for the function

Question 8

State the rule for the function

Answer 8

quick sketch

Question 9

State the rule for the function

Answer 9

Question 10

Answer 10

State the rule for the function

Question 11

State the rule for the function

Answer 11

quick sketch

Question 12

Answer 12

State the rule for the function

Question 13

What are the x-intercepts of y = sin(x) in the interval [0, 2π]?

Answer 13

x = 0, π, 2π

Question 14

What are the x-intercepts of y = cos(x) in the interval [0, 2π]?

Answer 14

x = π/2, 3π/2

Question 15

What are the x-intercepts of y = tan(x) in the interval [0, 2π]?

Answer 15

x = 0, π, 2π

Question 16

Find the x-intercepts of y = sin(x - π/2) in [0, 2π]

Answer 16

x = π/2, 3π/2

Question 17

Find the x-intercepts of y = cos(x - π/2) in [0, 2π]

Answer 17

x = 0, π, 2π

Question 18

Find the x-intercepts of y = tan(x - π/4) in [0, 2π]

Answer 18

x = π/4, 5π/4

Question 19

Find the x-intercepts of y = sin(2x) in [0, 2π]

Answer 19

x = 0, π/2, π, 3π/2, 2π

Question 20

Find the x-intercepts of y = cos(2x) in [0, 2π]

Answer 20

x = π/4, 3π/4, 5π/4, 7π/4

Question 21

Find the x-intercepts of y = tan(2x) in [0, 2π]

Answer 21

x = 0, π/2, π, 3π/2, 2π

Question 22

Find the x-intercepts of y = sin(x + π/3) in [0, 2π]

Answer 22

x = 2π/3, 5π/3

Question 23

Find the x-intercepts of y = cos(x + π/3) in [0, 2π]

Answer 23

x = π/6, 7π/6

Question 24

Find the x-intercepts of y = tan(x + π/3) in [0, 2π]

Answer 24

x = 2π/3, 5π/3

Question 25

Find the x-intercepts of f(x) = sin(x) + 1 in the interval [-2π, 2π]

Answer 25

x = -π/2, 3π/2

Question 26

Find the x-intercepts of f(x) = sin(x) - 1 in the interval [-2π, 2π]

Answer 26

x = -3π/2, π/2

Question 27

Find the x-intercepts of f(x) = cos(x) + 1 in the interval [-2π, 2π]

Answer 27

x = -π, π

Question 28

Find the x-intercepts of f(x) = cos(x) - 1 in the interval [-2π, 2π]

Answer 28

x = -2π, 0, 2π

Question 29

Find the x-intercepts of f(x) = tan(x) + 1 in the interval [-π, π]

Answer 29

x = -π/4, 3π/4

Question 30

Find the x-intercepts of f(x) = tan(x) - 1 in the interval [-π, π]

Answer 30

x = π/4, -3π/4

Question 31

Find the x-intercepts of f(x) = sin(x) + 1/2 in the interval [-2π, 2π]

Answer 31

x = -5π/6, -π/6, 7π/6, 11π/6

Question 32

Find the x-intercepts of f(x) = cos(x) - 1/2 in the interval [-2π, 2π]

Answer 32

x = -5π/3, -π/3, π/3, 5π/3

Question 33

Find the x-intercepts of f(x) = tan(x) + √3 in the interval [-π, π]

Answer 33

x = -π/3, 2π/3

Question 34

Find the x-intercepts of f(x) = tan(x) - √3 in the interval [-π, π]

Answer 34

x = π/3, -2π/3

Question 35

Find the x-intercepts of f(x) = sin(2x) in the interval [-π, π]

Answer 35

-π, -π/2, 0, π/2, π

Question 36

Find the x-intercepts of f(x) = sin(x/2) in the interval [-2π, 2π]

Answer 36

-2π, 0, 2π

Question 37

Find the x-intercepts of f(x) = cos(3x) in the interval [-π, π]

Answer 37

-5π/6, -π/2, -π/6, π/6, π/2, 5π/6

Question 38

Find the x-intercepts of f(x) = cos(x/4) in the interval [-2π, 2π]

Answer 38

-2π, 2π

Question 39

Find the x-intercepts of f(x) = tan(2x) in the interval [-π/2, π/2]

Answer 39

-π/2, 0, π/2

Question 40

Find the x-intercepts of f(x) = tan(x/2) in the interval [-π, π]

Answer 40

0

Question 41

Find the x-intercepts of f(x) = sin(3x/2) in the interval [-2π, 0]

Answer 41

-2π, -4/3π, -2/3π, 0

Question 42

Find the x-intercepts of f(x) = cos(3x/2) in the interval [0, 2π]

Answer 42

1/3π, 1π, 5/3π

Question 43

Find the x-intercepts of f(x) = tan(3x/2) in the interval [-π, 0]

Answer 43

-2/3π, 0

Question 44

Find the x-intercepts of f(x) = sin(4x) in the interval [-π/2, π/2]

Answer 44

-π/2, -π/4, 0, π/4, π/2

Question 45

Answer 45

Question 46

If finding the asymptotes of tan(f(x)) it can be easier to solve what?

Answer 46

cos(f(x))=0