Question

Find the amplitude, period, ohase shift, and endpoint then graph the following function.
a) y= cos2(x- pi/2) b) y= 2sin (1/2 x - pi/6)

Answer 1

If I'm not mistaken, the formulas are y = Asin(Bx C) + D and y = Acos(Bx C) + D?

Answer 2

yes for sin and cos

Answer 3

how do i find the amplitude?

Answer 4

The A is amplitude

Answer 5

so the amplitude is 2?

Answer 6

For letter b, yes.

Answer 7

and now i dont know how to find the period, phase shift, or endpoint.. are you familar with that?

Answer 8

for letter a, the amplitude is 1?

Answer 9

Yup, amp is 1
And it's been years since I've done period, phase, etc

Answer 10

Try: http://earthmath.kennesaw.edu/main_site/review_topics/ppsa_trig_functions.htm

Answer 11

im using that right now =/ no help

Answer 12

maybe @ranga can help you :)
I gtg so sorry :(

Answer 13

cos2(x- pi/2)
Is the 2 after cos an exponent or just a factor?

Answer 14

Good luck!

Answer 15

its not an exponent

Answer 16

its a whole number!

Answer 17

ok. take the 2 inside.
cos(2x - pi)
The period of the function Acos(Bx + C) is 2pi/B

So the period of cos(2x - pi) is 2pi/2 = pi

Do the same for the sine function.

Answer 18

but what is the amplitude because there is no number before the cos

Answer 19

A = 1 for cos

Answer 20

okay for letter b i got 3pi as the period

Answer 21

can you explain how to find phase shift and endpoint of letter a

Answer 22

period = 2pi/B
B = 1/2 for the second function
so period = 2p/(1/2) = 2pi * 2 = 4pi

Answer 23

oh whoops =X how do i find phase shif and endpoint for letter a

Answer 24

phase shift = c/b so theres no number before x what is b????

Answer 25

pi/2 ?

Answer 26

For Acos(Bx - C), phase shift is C/B
For cos2(x- pi/2)
C = pi/2 and B = 1
phase shift = pi/2

do the same for b)

Answer 27

i got pi/6 / 1/2

Answer 28

how do i do the math for that???

Answer 29

when you divide by a fraction, multiply by its reciprocal.

Answer 30

im sorry can you write that out for me?

Answer 31

pi/6 divided by 1/2 do i write that as p/6 * 2/1

Answer 32

yes. simplify.

Answer 33

what did you get as answer?

Answer 34

is it 2pi/6

Answer 35

simplify.

Answer 36

2 is a factor for both top and bottom.

Answer 37

im sorry i did not understand.. can you show me on the drawing

Answer 38

simplify 2pi/6

Answer 39

pi/3 ??

Answer 40

what is endpoint?

Answer 41

To find endpoint for cos2(x- pi/2)
solve the inequality:
0 <= 2(x- pi/2) <= 2pi
Solve both inequalities and find x.

Answer 42

can you show me pls

Answer 43

0 <= 2(x- pi/2) <= 2pi
divide by 2
0 <= x - pi/2 <= pi
add pi/2
pi/2 <= x <= 3/2pi
Those are the end points for a)

Do the same for b)

Answer 44

thank you! so muchhhh xx

Answer 45

do you know how to graph this function?

Answer 46

go to https://www.desmos.com/calculator
type in your function as cos2(x- pi/2) on the left column blank space and it will graph it for you.

Answer 47

thank you :)

Answer 48

you are welcome.