Question

Solve: sin^(2) x - Sin x =0, for 0≤x≤3

Answer 1

here we have to change variable, namely:
\[\Large \sin x = t\]

Answer 2

after that your equation can be rewritten as follows:
\[\Large {t^2} - t = 0\]

Answer 3

please solve that equation for t

Answer 4

So t=0?

Answer 5

hint, we can factor out t at left side, so we can write:
\[\Large t\left( {t - 1} \right) = 0\]

Answer 6

Oh, so t= 0 and 1?

Answer 7

that's right!

Answer 8

now
t=0 means:
sin x=0
what is x?

Answer 9

x= Radical 3 over 2?

Answer 10

Oops!

Answer 11

no, the solution of that equation:
sin x=0, are:
\[x = 0,\pi ,2\pi ,3\pi ...\]

Answer 12

nevertheless only x=0, is acceptable, since pi >3

Answer 13

Oh, i get it! Thank you!

Answer 14

please wait, we have to solve this equation:
t=1
which means
sin x =1

Answer 15

for which values x, we have:
sin x= 1?

Answer 16

\[\sin x = 1 \Rightarrow x = ...?\]

Answer 17

Pie over 2
and
3 pie over 2

Answer 18

no, the solutions are:
\[x = \frac{\pi }{2},2\pi + \frac{\pi }{2},4\pi + \frac{\pi }{2}...\]

Answer 19

Oh yea, my bad.

Answer 20

nevertheless only x= pi/2 is acceptable

Answer 21

I get it. thanks :D

Answer 22

thanks! :)