solvefor x,-1/(2y^2)=3sin(x)-1/8

Solution

solve for

x, - \frac{1}{2 y ^{2}} = 3 sin (x) - \frac{1}{8}

x = arcsin (\frac{- 4 + y ^{2}}{24 y ^{2}}) + 2 πn, x = π + arcsin (- \frac{- 4 + y ^{2}}{24 y ^{2}}) + 2 πn

Solution steps

- \frac{1}{2 y ^{2}} = 3 sin (x) - \frac{1}{8}

Switch sides

3 sin (x) - \frac{1}{8} = - \frac{1}{2 y ^{2}}

Move

\frac{1}{8}

to the right side

3 sin (x) = - \frac{1}{2 y ^{2}} + \frac{1}{8}

Divide both sides by

3

sin (x) = \frac{- 4 + y ^{2}}{24 y ^{2}}

Apply trig inverse properties

x = arcsin (\frac{- 4 + y ^{2}}{24 y ^{2}}) + 2 πn, x = π + arcsin (- \frac{- 4 + y ^{2}}{24 y ^{2}}) + 2 πn

sin (θ) = \frac{150 sin ( 11 5 ^{\circ} )}{212.6}

- sin (x) - sin (2 x) = 0

2 cos^{2} (2 x) + cos (2 x) - 1 = 0

cos (θ) = \frac{0}{8}

3 sin (x) + 2 = 1