What is the general solution for 10=14+8sin((pit)/(12)) ?

The general solution for 10=14+8sin((pit)/(12)) is t=14+24n,t=22+24n

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10=14+8sin((pit)/(12))

10 = 14 + 8 sin (\frac{π t}{12})

t = 14 + 24 n, t = 22 + 24 n

Solution steps

10 = 14 + 8 sin (\frac{π t}{12})

Switch sides

14 + 8 sin (\frac{π t}{12}) = 10

Move

14

to the right side

8 sin (\frac{π t}{12}) = - 4

Divide both sides by

8

sin (\frac{π t}{12}) = - \frac{1}{2}

General solutions for

sin (\frac{π t}{12}) = - \frac{1}{2}

\frac{π t}{12} = \frac{7 π}{6} + 2 πn, \frac{π t}{12} = \frac{11 π}{6} + 2 πn

Solve

\frac{π t}{12} = \frac{7 π}{6} + 2 πn : t = 14 + 24 n

Solve

\frac{π t}{12} = \frac{11 π}{6} + 2 πn : t = 22 + 24 n

t = 14 + 24 n, t = 22 + 24 n

sin (4 x) cos (x) - cos (4 x) sin (x) = 1

sec (θ) = \frac{10}{6}

x, 2 cos (3 x) = - 3

x, 7 - 3 cos (x) = 9 sin^{2} (x)

4 sin (x) = 3 tan (x)

What is the general solution for 10=14+8sin((pit)/(12)) ?
The general solution for 10=14+8sin((pit)/(12)) is t=14+24n,t=22+24n