What is the general solution for 120=23sin(pi/6 (x))+107 ?

The general solution for 120=23sin(pi/6 (x))+107 is x=(6*0.60069…)/pi+12n,x=6-(6*0.60069…)/pi+12n

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120=23sin(pi/6 (x))+107

120 = 23 sin (\frac{π}{6} (x)) + 107

x = \frac{6 \cdot 0.60069 \dots}{π} + 12 n, x = 6 - \frac{6 \cdot 0.60069 \dots}{π} + 12 n

Solution steps

120 = 23 sin (\frac{π}{6} (x)) + 107

Switch sides

23 sin (\frac{π}{6} x) + 107 = 120

Move

107

to the right side

23 sin (\frac{π}{6} x) = 13

Divide both sides by

23

sin (\frac{π}{6} x) = \frac{13}{23}

Apply trig inverse properties

\frac{π}{6} x = arcsin (\frac{13}{23}) + 2 πn, \frac{π}{6} x = π - arcsin (\frac{13}{23}) + 2 πn

Solve

\frac{π}{6} x = arcsin (\frac{13}{23}) + 2 πn : x = \frac{6 arcsin ( \frac{13}{23} )}{π} + 12 n

Solve

\frac{π}{6} x = π - arcsin (\frac{13}{23}) + 2 πn : x = 6 - \frac{6 arcsin ( \frac{13}{23} )}{π} + 12 n

x = \frac{6 arcsin ( \frac{13}{23} )}{π} + 12 n, x = 6 - \frac{6 arcsin ( \frac{13}{23} )}{π} + 12 n

Show solutions in decimal form

x = \frac{6 \cdot 0.60069 \dots}{π} + 12 n, x = 6 - \frac{6 \cdot 0.60069 \dots}{π} + 12 n

4 sin (3 θ) = 2

cos (x) = cos (3 x) + 2 sin (2 x)

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

\frac{700}{sin ( 9 0 ^{\circ} )} = \frac{236.3277}{sin ( θ )}

cos (x) + cos (2 x) = - 0.75

What is the general solution for 120=23sin(pi/6 (x))+107 ?
The general solution for 120=23sin(pi/6 (x))+107 is x=(6*0.60069…)/pi+12n,x=6-(6*0.60069…)/pi+12n