Question

simplify using identities so that you can solve the equation. Give the general solution in radians.

sin x = 1 - 2 cos^2 x

Answer 1

Have you considered \(\cos^{2}(x) = 1 - \sin^2(x)\)?

Answer 2

but what do I do to get the answer in radians?

Answer 3

Do as tkhunny said
then Factorize....

sinx = 1- 2 (1-sin^2(x))

sinx = 1 - 2 +2sin^2(x)

2sin^2(x) - sinx - 1 = 0

(2sinx + 1)(sinx - 1) = 0

sinx = 1
sinx = -0.5

Answer 4

To get the answer in radians you just put in pi/2 instead of 90° for sinx=1 for example.
Or you set you calculator to radians when doing x=sin^-1(-1/2)

Answer 5

thank you!

Answer 6

You simply solve the equation. Why would it be in anything but Radians? BTW "Radians" aren't really a unit of anything. They are just numbers.

\(\sin(x) = 1 \implies x = \dfrac{\pi}{2} + 2k\pi\; for\; k\;an\;integer.\) There are infinitely many such solutions.