Question

How would you solve sin^2x=sinx without graphing it?

Answer 1

\[\sin^2(x) = (\sin(x))^2\]

so dividing both sides by sin(x)

gives sin(x) = 1

Answer 2

It's just sin^2x=sinx, not =sinx^2

Answer 3

Oh, NVM
I see what ou meant.

Answer 4

So then you would take the arcsin of 1?

Answer 5

yes.

gotta love brackets <3 :P

Answer 6

lol

Answer 7

if you just divide by sin(x) then you will miss one of the solutions. you need to take the sin(x) from the right-hand-side to the left and factor as follows:\[\sin^2(x)=\sin(x)\]\[\therefore \sin^2(x)-\sin(x)=0\]\[\therefore \sin(x)(\sin(x)-1)=0\]solve from there

Answer 8

Okay. How would you know if you are missing a sollution?

Answer 9

because you divided by sin(x) - that means you have thrown away one solution which is sin(x)=0

Answer 10

Can you give me an example?

Answer 11

lets say you were given:\[x^2=x\]and you just divided both sides by x to get:\[x=1\]here you have missed the solution x=0

Answer 12

where as:\[x^2=x\]\[x^2-x=0\]\[x(x-1)=0\]\[x=0\qquad\text{or}\qquad x=1\]

Answer 13

Okay, so you never divide by both sides when it comes to these types of problems, right?

Answer 14

correct

Answer 15

Set it =0?

Answer 16

Then simplify?

Answer 17

asnaseer is right.

my bad

Answer 18

np.

Answer 19

no worries @Euler271 - we all make mistakes sometimes - that is what makes us human. :)

Answer 20

Guys, can you go through with me on the next problem, tell me if I made a mistake?

Answer 21

ya

Answer 22

sure - just post it as a new question please.

Answer 23

Okay.