[Periodic Functions and Applications]

Solve sin^2x=1/4 for 0

Question

[Periodic Functions and Applications]

Solve sin^2x=1/4 for 0<x<360

Can someone please walk me through how to solve this one? :)

gunsodo · Answer

From sin^2x=1/4
So sinx = 1/2
You could continue by looking up for formulas

kayla0297 · Answer

Hmmm I got that far, then first solution is 30degrees, the second is 150degrees...? There must be something else I am missing, as the textbook lists two other values :S

parthkohli · Answer

$$\sin^2 x = 1/4 \implies \sin(x) = \pm 1/2$$

parthkohli · Answer

Remember that the square of $-1/2$

parthkohli · Answer

is also $1/4.$

kayla0297 · Answer

Ah, so while 30 and 150 degrees are the solutions when sin is positive, having sin^2x means that I must also find solutions when sin is negative?

parthkohli · Answer

Indeed.

kayla0297 · Answer

Okay, thanks for the help!

parthkohli · Answer

What did you get for the negative values?

And no problem!

kayla0297 · Answer

210 and 330 degrees

parthkohli · Answer

That is correct.

anonymous · Answer

YES