Question

Find the amplitude and period of f (x) = −2 cos(1/3x + 1

Answer 1

the amplitude is the coefficient of the function, that is 2

Answer 2

rewrite cos(1/3x + 1)=cos1/3[(x) +3]

Answer 3

Then the period will be 2pi/1/3 or 6 pi

Answer 4

thanks can you help
Find the angle co-terminal with 23pi/3

Answer 5

23pi/3 = 7 and 2/3 pi. Since each revolution is 2 pi, we make 3 complete revolutions and then 1 2/3 pi more or 5/3 pi. So the angle that is co-terminal with 23pi/3 is 5/3 pi

Answer 6

i dont have 5pi/3 as an option

Answer 7

It could be - pi/3

Answer 8

yeah i have that option

Answer 9

-pi/3 is the same as 5pi/3

Answer 10

how do you convert from 5pi/3 to -1pi/3

Answer 11

5pi/3 - 2pi

Answer 12

ok i see

Answer 13

Good

Answer 14

you think you can help me with this one too?
Find the exact value of cot (sin^-1 (sqrt2/2))

Answer 15

(sin^-1 (sqrt2/2) meant the angle whose sin is sqrt2/2 which is pi/4 or 3pi/4

Answer 16

so now the problem becomes cot(pi/4) which is 1 or cot(3pi/4) which is -1.

Answer 17

You might want to reread your directions carefully. If you have to give ALL the angles for which this is true, you would have to say pi/4 +k2pi and 3pi/4 +k2pi

Answer 18

Do you understand?

Answer 19

yea

Answer 20

for my options i have
a) pi/4
b) -pi/4
c) 0
d) -1
e) 1

i have to pick between 1 and -1...how do i decide

Answer 21

Are we still talking about the same problem?

Answer 22

yea

Answer 23

Well then, I would go with 1 because I am assuming that you are a beginner in trig. If that right?

Answer 24

Is that right?

Answer 25

yea

Answer 26

So go with 1

Answer 27

ok kool. i have no way of telling whether its right or wrong. im just going over practice questions for a test but i understand the concept

Answer 28

Good for you.

Answer 29

Simplify sin 2k cos k + cos 2k sin k using an appropriate trigonometric identify.

do you know this one?

Answer 30

This looks like the formula:
sin(x+y) = sin(x)cos(y)+ cos(x)sin(y)
sin(2k)cos(k) + cos(2k)sin(k)

Answer 31

It matches up so it would be sin(2k+k)=sin(3k)

Answer 32

yea that looks right
how about

sinx + (cos^2x)/(sinx)

Answer 33

Well, cos^2(x) = 1-sin^2(x) so if we make that substitution we would have
sin(x) + 2-sin^2(x) /sin x

Answer 34

Is the entire thing over sin(x) or just the cos^(x)?

Answer 35

just the cos^(x) and we are simplyfing i forgot to mention that