Trig Functions and Graphs

Question 1

Vertical dilation of y=f(x)

Answer 1

y=kf(x) - scale factor k

Question 2

If k>0

Answer 2

the function is stretched vertically

Question 3

If 0

Answer 3

the function is compressed vertically

Question 4

If k = -1

Answer 4

the function is reflected in the x-axis

Question 5

What is the amplitude

Answer 5

the height from the centre of the periodic function to the maximum or minimum value

Question 6

What is a horizontal dilation of y = f(x)

Answer 6

y=f(ax) - scale factor 1/a

Question 7

If a > 0

Answer 7

the function is stretched

Question 8

If 0<a></a>

Answer 8

the function is compressed

Question 9

If a = -1

Answer 9

the function is reflected in the y-axis

Question 10

What is a period

Answer 10

The length of one cycle of a periodic function on the x-axis

Question 11

Period of cosx and sinx

Answer 11

Given y=sin(ax),

2 π/a

Question 12

Period of tanx

Answer 12

Given y=tan(ax)

π/a

Question 13

Vertical translation of y=f(x)

Answer 13

y=f(x) +c

Question 14

If c>0

Answer 14

centre is translated up

Question 15

If c<0

Answer 15

centre is translated down

Question 16

Horizontal translation =

Answer 16

phase shift

Question 17

What is the phase of y=sin/cos/tan

Answer 17

b:
y=sin(x+b)
y=cos(x+b)
y=tan(x+b)

Question 18

If b > 0

Answer 18

the phase shift is to the left

Question 19

If b<0

Answer 19

the phase shift is to the right

Question 20

What is a phase

Answer 20

angle where x=0
(let x =0 to find phase)

Question 21

What order to apply transformations in

Answer 21

Start with standard base function (y=sin/cos/tanx)

1. Dilations
2. Translations

Question 22

How to solve trig equations graphically

Answer 22

Treat each side of function as a separate function
graph each function separately
solution - x-value where the graphs intersect

Question 23

How to solve trig equations algebraically

Answer 23

Find the new domain (e.g 2x –> domain=0<2x<720)
Use all stations to central to find all angles in new domain
Find values of x

Question 24

How to solve trig equations algebraically with a phase shift

Answer 24

Find the new domain by using an inequality with (x+phase) in the centre
Then solve the same way and solve for x, ensuring all angles are in the new domain

Question 25

What type of functions are sinx and tanx

Answer 25

``` odd functions (therefore have point symmetry in the origin) ```

Question 26

sin(-x)=

Answer 26

-sinx

Question 27

tan(-x)=

Answer 27

-tanx

Question 28

What type of function is cosx

Answer 28

``` even function (therefore has line symmetry in the y-axis) ```

Question 29

cos(-x)=

Answer 29

-cosx

Question 30

Good job your doing great:)

Answer 30

:)