How to Solve Trigonometric Equation sin2x = sqrt(2)/2 Using Algebra?

[manish00333]

Solve sin2x= sqrt(2)/2 (using algebra)
the interval is between 0 and 2pi

i got the first two answers: pi/8 and 3pi/8, but i don t understand how to get the other two: 9pi/8 and 11pi/8.

thanks!

 

[MarkFL]

If we are told:

$$0\le x<2\pi$$

then:

$$0\le 2x<4\pi$$

 

[manish00333]

Oh, that makes sense!

So, pi/4 + 2pi = 9pi/4
and 3pi/4 + 2pi = 11pi/4

and when i divide them by 2, i get 9pi/8 and 11pi/8.

thank you so much! :D

 

[MarkFL]

So, pi/4 + 2pi = 9pi/4
and 3pi/4 + 2pi = 11pi/4

and when i divide them by 2, i get 9pi/8 and 11pi/8.

Perfect! (Yes)