Question

http://prntscr.com/d4szih @tkhunny

Answer 1

who doesnt like noodles

Answer 2

oh hi @tkhunny

Answer 3

Well, simplify and solve.

\(15 = 17 + 4\cos\left(\dfrac{y}{y}\right)\) - Go! What's first?

Answer 4

well, im not really sure this is my first time doing trig

Answer 5

i would say parentheses?

Answer 6

Whoops. Should be y/7.

cosines come in [-1,1]. Until we have that sort of range, there is no sense doing anything else. Try subtraction and division, first and second.

Answer 7

subtract 4 from both sides?

Answer 8

Please solve the following for z

15 = 17 + 4z

Answer 9

z= -1/2?

Answer 10

Okay, now do the same thing. Please solve for cos(y/7).

Answer 11

what is "cos"

Answer 12

Do you have an original problem statement?

Answer 13

Without using a calculator find the solution(s) to the following equations. If an interval is given then find only those solutions that are in the interval. If no interval is given then find all solutions to the equation.

Answer 14

What equation are we trying to solve? I don't recall changing problems from

15 = 17 + 4cos(y/7)

Answer 15

^ that is the equation

Answer 16

that is just the directions

Answer 17

There you go. Solve that for the cosine EXACTLY like you solved it for 'z'.

Answer 18

y=14?

Answer 19

or -14

Answer 20

so it would be 2=2 at the end

Answer 21

Where did the cosine go?

Answer 22

oh the cos is still there

Answer 23

um

Answer 24

does cos have a value?

Answer 25

cosine is a function. You can't divide by it. You are required to understand it.

15 = 17 + 4cos(y/7)
-2 = 4cos(y/7)
-1/2 = cos(y/7)

Where is the cosine equal to -1/2? There are two places on \([0,2\pi]\). Consult your unit circle.

Answer 26

60 degrees? π/3?

Answer 27

or is that for positive 1/2

Answer 28

i dont have a unit circle

Answer 29

https://en.wikipedia.org/wiki/Unit_circle
Everything is positive in Quadrant I.

Answer 30

i am so confused, sorry

Answer 31

cos and sin are put in quadrant 2 in the picture of unit circle

Answer 32

Did you find the two places where cosine is -1/2? Scroll down the page to right before the [See Also]. It's all red and blue. Find the two locations where the x-coordinate is -1/2.

Answer 33

yes i see it in quadrant 3 at 210 and 240 degrees @tkhunny

Answer 34

I'll give you 240º, or 4pi/3.
The other is 120º or 2pi/3.
Do you see them both and have them properly identified?

Answer 35

yes sir

Answer 36

Solutions are \(2\pi/3 + 2k\pi\) AND \(4\pi/3 + 2k\pi\) where k is any integer. There are infinitely many of them.

This is because the cosine is a periodic function. The period is \(2\pi\)

This means you get to write:

y/7 = \(2\pi/3 + 2k\pi\)
or
y/7 = \(4\pi/3 + 2k\pi\)

This is how you understand and eliminate the cosine function. You now have many, many solutions. Next, find some expressions for y, instead of y/7.

Answer 37

i think im going to take a shot of bleach

Answer 38

if we eliminated the cosine function doesnt that mean we can just solve like regular

Answer 39

If you can multiply by 7 correctly, you will be very close to a final solution. Carefully!

Answer 40

okay multiplying by 7 isolates the y

Answer 41

i multiply the other side by 7 too?

Answer 42

I hope. Have you EVER solved doing anything else?

Answer 43

not really

Answer 44

never!!

Answer 45

Okay, let's see it.

Answer 46

-1/2 times 7?

Answer 47

i assume we start from that place

Answer 48

-3.5=y

Answer 49

?

Answer 50

Why would you do that? We went to all that trouble to get rid of the cosine and you just brought it back. Don't do that. Start right after "This means you get to write:"

Answer 51

4pi divided by 3?

Answer 52

do we have to solve with pi

Answer 53

or just keep the pi as the symbol

Answer 54

It's just a number. Just write it and move on. \(\pi\) multiplied by 7 is \(7\pi\). Simple as that.

Answer 55

28π /21 +14kπ

Answer 56

you have to multiply 7 to all of them right

Answer 57

Where did the 21 come from? Numerators only, please. Do both pieces. You will need both of them to complete the problem.

Answer 58

21 came from the 3

Answer 59

numerators only would be 28π / 3 +14π k?

Answer 60

No, it didn't. 21 came from the sky. The 3 should still be there.

7 * (4/3) = 28/3 not 28/21

Answer 61

yes it came from outside the universe, im sorry

Answer 62

i understand that part now

Answer 63

And the other piece?

Answer 64

you are very patient, thank you for understanding that i am not the greatest with math

Answer 65

the other piece with the 2π? that would be 14π/3 + 14kπ

Answer 66

I appreciate you hanging in there. I can be perceived as a little cranky. I'm not, really. :-)

That's exactly correct. See, you're fine at math.

Your last task, is to fine the value of k that puts these guys in the selected range, \([10\pi,15\pi]\)

Answer 67

wait a sec wouldnt 1 work

Answer 68

you aren't really cranky, u are quite nice, i like you, be my friend

Answer 69

they have to be between 10π and 15π ?

Answer 70

Both may have solutions

30/3pi = 10π <= 14π/3 + 14kπ <= 16π = 48/3π

16/3pi <= 14kπ <= 34/3π

16/42 <= k <= 34/42 -- Any integers in there?

Do the same things with the other expression.

Answer 71

are you saying 30/3pi = 10π <= 14π/3 + 14kπ <= 16π = 48/3π are equal?

Answer 72

<= means "less than or equal to".

I am saying that 30/3pi = 10pi and that 48/4pi = 16pi

Answer 73

OHH

Answer 74

so u did the first expression? is the second expression 16/3pi <= 14kπ <= 34/3π

Answer 75

im not sure if i understand where u got the expressions from :(

Answer 76

I just subtracted 14/3pi from all three pieces.
Then I divided all three pieces by 14pi. Everything is positive, so that's okay.

Okay, I have to go. Good luck with that other piece. I hope you find an integer solution.

Answer 77

thank you @tkhunny have a nice day

Answer 78

i will try to figure out the rest

Answer 79

oh btw if you happen to have the time, check out my profile :) i think it will make you smile @tkhunny