Graphs

Question 1

sin period

Answer 1

2π

Question 2

cos period

Answer 2

2π

Question 3

cos is sin shifted by…

Answer 3

π/2

Question 4

sinusoidal function range

Answer 4

[-1, 1]

Question 5

sin is symmetrical with respect to the…

Answer 5

origin

Question 6

cos is symmetrical with respect to the…

Answer 6

y-axis

Question 7

new period formula for transformed sinusoidal function

Answer 7

period = 2π/|B|

Question 8

critical points are given by…

Answer 8

period/4

Question 9

amplitude of tan is found at…

Answer 9

1/4 the period

Question 10

tan period

Answer 10

π

Question 11

tan vertical asymptotes

Answer 11

x = π/2 + πk

where K is any integer

Question 12

new period formula for transformed tan

Answer 12

period = π/|B|

Question 13

cot vertical asymptotes

Answer 13

x = π + πk

where k is any integer

Question 14

—– and —- have a vertical asymptotes on the y-axis

Answer 14

cotangent
cosecant

Question 15

sec period

Answer 15

2π

Question 16

sec vertical asymptotes

Answer 16

x = π/2 + πk

where k is any integer

Question 17

range of sec

Answer 17

(-∞,-1]U[1,∞)

Question 18

new period formula for transformed sec

Answer 18

period = 2π/|B|

Question 19

csc period

Answer 19

2π

Question 20

csc vertical asymptotes

Answer 20

πk

where k is any integer

Question 21

domain restriction to take inverse of sin

Answer 21

[-π/2, π/2]

Question 22

domain restriction to take inverse of cos

Answer 22

[0, 1]

Question 23

domain restriction to take inverse of tan

Answer 23

(-π/2, π/2)

Question 24

interval for sin(sin-1x) = x

Answer 24

-1≤ x ≤ 1

Question 25

interval for cos(cos-1x) = x

Answer 25

-1≤ x ≤ 1

Question 26

interval for tan(tan-1x) = x

Answer 26

(-∞, ∞)

Question 27

interval for sin-1(sinx) = x

Answer 27

-π/2 ≤ x ≤ π/2

Question 28

interval for cos-1(cosx) = x

Answer 28

0 ≤ x ≤ π

Question 29

interval for tan-1(tanx) = x

Answer 29

-π/2 < x < π/2