Study

Question 1

When is cos 0?

Answer 1

Every π/2

Question 2

0 every π/2

Answer 2

cos

Question 3

When is sin 0?

Answer 3

Every π

Question 4

0 every π

Answer 4

sin

Question 5

What kind of functions are sin and cos?

Answer 5

sin is odd and cos is even

Question 6

Periods of sin and cos

Answer 6

2π

Question 7

2π is the period of

Answer 7

sin and cos

Question 8

Form of sinusoidal function

Answer 8

f(x) = a sin[b(x-c)] + d

or

f(x) = a cos[b(z-c)] + d

Question 9

f(x) = a sin[b(x-c)] + d

or

f(x) = a cos[b(z-c)] + d

Answer 9

Sinusoidal functions

Question 10

What is the range of y = a sinx and y = a cosx?

Answer 10

(-a,a)

Question 11

(-a,a)

Answer 11

Range of y = a sinx and y = a cosx

Question 12

What is the period of y =sinbx or

y = cosbx

Answer 12

2π/b

Question 13

2π/b

Answer 13

period of y =sinbx or

y = cosbx

Question 14

With sinusoidal functions, a horizontal shift is called

Answer 14

Phase shift

Question 15

Phase shift

Answer 15

Horizontal shift in sinusoidal function

Question 16

If a < 0 in a sinusoidal function

Answer 16

|a| is amplitude and function is reflected across x-axis

Question 17

|a| is amplitude and function is reflected across x-axis

Answer 17

If a < 0 in sinusoidal function

Question 18

What is the cycle of a graph

Answer 18

x values for which one complete repetition of the graph is completed

Question 19

x values for which one complete repetition of the graph is completed

Answer 19

Cycle

Question 20

Domain and range of tan graph

Answer 20

Every number except intervals of π/2 and range is all reals

Question 21

Zeros of tan function

Answer 21

Every π

Question 22

Has zeros at every π

Answer 22

Tan function

Question 23

For tan graphs, divide interval into equal parts of length

Answer 23

1/4 • π/b

Question 24

1/4 • π/b

Answer 24

Tan graph intervals

Question 25

Locate adjacent asymptotes

Answer 25

b(x-c)=-π/2 and b(x-c)= π/2

Question 26

b(x-c)=-π/2 and b(x-c)= π/2

Answer 26

Locate adjacent asymptotes

Question 27

Domain and range of csc x

Answer 27

Domain: asymptote every π Range: (-∞,-1] U [1, ∞)

Question 28

Domain: asymptote every π Range: (-∞,-1] U [1, ∞)

Answer 28

csc x

Question 29

Domain and range of sec x

Answer 29

Domain: asymptote every π/2 Range: (-∞,-1] U [1, ∞)

Question 30

Domain: asymptote every π/2 Range: (-∞,-1] U [1, ∞)

Answer 30

Domain and range of sec x

Question 31

Even or odd?: csc, sec, cot

Answer 31

Odd, even, odd

Question 32

Inverse function is defined by

Answer 32

y = sin^-1x iff x = siny

Question 33

y = sin^-1x iff x = siny

Answer 33

Inverse function

Question 34

x = siny for

Answer 34

-1 <= x <= 1 and -π/2 <= y <= π/2

Question 35

y = cos^-1x iff x = cos y for

Answer 35

-1 <= x <= 1 and 0 <= y <= π

Question 36

-1 <= x <= 1 and 0 <= y <= π

Answer 36

y = cos^-1x iff x = cos y for

Question 37

y = tan^1 x iff x = tan y for

Answer 37

All reals and -π/2 <= y <= π/2

Question 38

All reals and -π/2 <= y <= π/2

Answer 38

y = tan^1 x iff x = tan y for

Question 39

Why is cos^-1[cos(5π/4)] 3π/4?

Answer 39

Because arccos can only be in second quadrant or first and subtracting π from 5π/4 gives a reference angle in the second quadrant

Question 40

How are the intervals of a graph identified?

Answer 40

Divide period by 4

Question 41

Divide period by 4

Answer 41

Identifying intervals of a graph