Question

Using double and identities, find the exact solutions for 0 11 years ago

Answer 1

let met try, i haven't done this in awhile
sin2x=root3sinx
2sinxcosx=root3sinx
divide by sinx
2cosx=root3
divide by 2
cosx=root3/2
x=pi/6, 5pi/6

Answer 2

i hope that's the anwser, i got rusty in this

Answer 3

Thank you so much! I thought sin2x was sinx + cosx, (silly mistake, thats pythagorean) not multiplying the 2.

Answer 4

actually the solution are x=0. pi, pi/6

Answer 5

i just checked it by unit circle

Answer 6

you're welcome

Answer 7

how did you get x=0 and pi?

Answer 8

Sorry yesterday i went to sleep
Here the steps
before i missed a step and missed some solutions
because it isn't allowed to divide by sinx since it could equal zero too which not allowed in the denumerator
so it is as follwed:
sin2x=root3sinx
substract root3sinx from both sides
-root3sinx+sin2x=0
use the indentity sin2x=2sinxcosx
-root3sinx+2sinxcosx=0
factor sinx
sinx(-root3+2cosx)=0
then sinx=0 or -root3+2cosx=0
sinx=0 or 2cosx=root3
sinx=0 or cosx=root3/2
now solve
we get
x=0, pi or x=pi/6
we cannot go further since the interval is 0<= x <= pi