Question

Solve the following equation for theta where
0 < or= theta < 2 pie

sin ^2 theta = sin theta

Answer 1

\[\sin^2(\theta)-\sin(\theta)=0\]
factor left hand side

Answer 2

is that (sin theta) (sin theta)???

Answer 3

yes x^2 can be written as x*x

Answer 4

so... now what?

Answer 5

factor

Answer 6

\[x^2-x \\ x(x-1)\]
you try factoring
\[\sin^2(\theta)-\sin(\theta)\]
it is the same way as I did the expression of x

Answer 7

\[x^2=x \\ x^2-x=0 \\ x(x-1)=0 \\ \text{ set both factors equal to zero } \\ x=0 \text{ or } x-1=0 \\ x=0 \text{ or } x=1 \]

Answer 8

you try solving for sin(theta) now
it is the same way

Answer 9

once you have solved for sin(theta)
then you will easily be able to find theta

Answer 10

hold on, don't leave yet

Answer 11

sin =0
sin theta = 0

Answer 12

I have no idea what to do next

Answer 13

well you have one equation correct
but you are missing an equation

Answer 14

have you not factored \[\sin^2(\theta)-\sin(\theta)\]
yet?

Answer 15

do you see both sin^2(theta) and sin(theta) have a common factor?

Answer 16

as you said sin^2(theta) can be written as sin(theta)*sin(theta)

therefore sin(theta) and sin^2(theta) both have the common factor sin(theta)

Answer 17

so you can factor that out of the expression

Answer 18

\[\sin^2(\theta)-\sin(\theta)=0 \\ \sin(\theta)(\sin(\theta)-1)=0\]
that is what you should get for the left hand side after factoring
now set both factors equal to 0

Answer 19

you can use the unit circle to solve both equations

Answer 20

wait hold on

Answer 21

where did you get these 2 equations?

Answer 22

which two?

Answer 23

wait nvm

Answer 24

ok but how do you use the unit circle for this?
i'm lost

Answer 25

do you know which equations you are solving?

Answer 26

sin^2 theta - sin theta = 0

Answer 27

you need to factor the left hand side

Answer 28

I have actually done this for you

Answer 29

I know x factor, but don't know how

Answer 30

now set both factors equal to 0

Answer 31

you have sin(theta)=0 or sin(theta)-1=0

Answer 32

find when sin(theta) is 0 on the unit circle

find when sin(theta) is 1 on the unit circle

Answer 33

in other words you are looking for where the y-coordinate is 0 on the unit circle

and also looking for when the y coordinate is 1 on the unit circle

Answer 34

the answer is pie/2 and pie

Answer 35

but how is it pie though???

Answer 36

nvm

Answer 37

got it

Answer 38

so you don't get that sin(pi)=0?


also sin(0)=0

so I think you mean you have 0,pi/2,pi

Answer 39

ok thx