0=1+2sin((x^2)/2)

Solution

0 = 1 + 2 sin (\frac{x ^{2}}{2})

x = \frac{7 π + 12 πn}{3}, x = - \frac{7 π + 12 πn}{3}, x = \frac{11 π + 12 πn}{3}, x = - \frac{11 π + 12 πn}{3}

Solution steps

0 = 1 + 2 sin (\frac{x ^{2}}{2})

Switch sides

1 + 2 sin (\frac{x ^{2}}{2}) = 0

Move

1

to the right side

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

Divide both sides by

2

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

General solutions for

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

\frac{x ^{2}}{2} = \frac{7 π}{6} + 2 πn, \frac{x ^{2}}{2} = \frac{11 π}{6} + 2 πn

Solve

\frac{x ^{2}}{2} = \frac{7 π}{6} + 2 πn : x = \frac{7 π + 12 πn}{3}, x = - \frac{7 π + 12 πn}{3}

Solve

\frac{x ^{2}}{2} = \frac{11 π}{6} + 2 πn : x = \frac{11 π + 12 πn}{3}, x = - \frac{11 π + 12 πn}{3}

x = \frac{7 π + 12 πn}{3}, x = - \frac{7 π + 12 πn}{3}, x = \frac{11 π + 12 πn}{3}, x = - \frac{11 π + 12 πn}{3}

cos (2 x) - 5 cos (x) + 3 = 0

9 sin^{2} (x) + 18 sin (x) + 9 = 0

- 12 sin^{2} (θ) + 7 = 4

4 cos (θ) + 5 = 0

cos (θ) = \frac{60}{78}