Question

PLEASE HELP!!!
Solve the equation.
sin^2 x + sin x = 2

Answer 1

Confused on how to start this one? :o

Answer 2

Yeah...

Answer 3

Would you know how to solve this equation if you given it?
\(\large\rm u^2+u=2\)
solve for u?

Answer 4

Oh! Use it like the quadratic formula?

Answer 5

Yessss. Good good good.

Answer 6

So, then I'd subtract two from both sides..
And for my problem I'd treat sin as x

Answer 7

Well we already have x in the problem,
maybe us another letter? :3

Answer 8

Treat \(\rm\sin x\) as \(\rm u\) maybe? :)

Answer 9

so u^2 + u = -2

Answer 10

And it would factor out to (u-1) and (u+2)

Answer 11

u^2+u-2=0 is what you meant to write, yes?
Ok factors look good!

Answer 12

Yeah, thats what I meant.

Answer 13

So, then U = -2 and U = 1

Answer 14

But I don't understand how to use that

Answer 15

Ok great, let's "undo" the replacement we made earlier.

Answer 16

sinx = -2 and sinx = 1 ?

Answer 17

Yessss.
Can you think of angles that would give us these values?
If they exist.

Answer 18

I can't think of any..

Answer 19

sine is your y-coordinate.
y-coordinate = 1 at which angle? :)

Answer 20

the full length

Answer 21

Oh! sin x = 1 at pi/2

Answer 22

Ok good :)

Answer 23

So if sin x = -2, that's just showing that it makes more revolutions?

Answer 24

Hmm not quite :)

Recall that your sine function can only output values between -1 and 1.
So -2 is outside of that range.

So therefore sinx=-2 gives no solution.

Answer 25

Wait..

Answer 26

But sin can't be more than one or less than negative one.. right?

Answer 27

So would the other answer be extranous?

Answer 28

ya sorry i spilled the beans :3 bahhh i gotta type slower, sorry

Answer 29

It's all good! I'm just really slow sometimes. Thanks for all your help!

Answer 30

extraneous is when we find a solution,
and then discover that it doesn't work for the original problem.

In this case, we are unable to find a solution.
So it's a little different than extraneous, but yes same type of idea ^^

Answer 31

Oh! So extraneous is when we plug it back in, but it doesn't work?

Answer 32

yes

Answer 33

Thank you much!

Answer 34

oh oh oh

Answer 35

So yes, pi/2 is a solution.
But what happens when we spin another time around the circle, landing up at pi/2 again. This new angle would be pi/2 + 2pi.

This also gives us 1 when we take the sine of it, right?

Answer 36

so it would be 90 and 450 degrees?

Answer 37

Well, what if we spun around the circle twice and landed at the same spot,
810 degree angle should work also, yes?

Answer 38

so i would add + 2pi n?

Answer 39

We have to allow for rotations. (Unless the question specified an interval)

Answer 40

Yes, good.

\(\large\rm \sin(x)=1\)
therefore
\(\large\rm x=\frac{\pi}{2}+2\pi n\)
Where n is an integer.

Answer 41

Or if you prefer degrees,
x=90+360n

Answer 42

Yay! I finally get it now!!

Answer 43

yay \c:/