What is the general solution for 12cos(pi/3 x)+8=0 ?

The general solution for 12cos(pi/3 x)+8=0 is x=(3*2.30052…)/pi+6n,x=-(3*2.30052…)/pi+6n

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12cos(pi/3 x)+8=0

12 cos (\frac{π}{3} x) + 8 = 0

x = \frac{3 \cdot 2.30052 \dots}{π} + 6 n, x = - \frac{3 \cdot 2.30052 \dots}{π} + 6 n

Solution steps

12 cos (\frac{π}{3} x) + 8 = 0

Move

8

to the right side

12 cos (\frac{π}{3} x) = - 8

Divide both sides by

12

cos (\frac{π}{3} x) = - \frac{2}{3}

Apply trig inverse properties

\frac{π}{3} x = arccos (- \frac{2}{3}) + 2 πn, \frac{π}{3} x = - arccos (- \frac{2}{3}) + 2 πn

Solve

\frac{π}{3} x = arccos (- \frac{2}{3}) + 2 πn : x = \frac{3 arccos ( - \frac{2}{3} )}{π} + 6 n

Solve

\frac{π}{3} x = - arccos (- \frac{2}{3}) + 2 πn : x = - \frac{3 arccos ( - \frac{2}{3} )}{π} + 6 n

x = \frac{3 arccos ( - \frac{2}{3} )}{π} + 6 n, x = - \frac{3 arccos ( - \frac{2}{3} )}{π} + 6 n

Show solutions in decimal form

x = \frac{3 \cdot 2.30052 \dots}{π} + 6 n, x = - \frac{3 \cdot 2.30052 \dots}{π} + 6 n

\frac{sin ( 4 5 ^{\circ} )}{497.01} = \frac{sin ( x )}{450}

\frac{35}{sin ( A )} = \frac{60}{sin ( 2 5 ^{\circ} )}

4 csc (x) + sin (x) + 5 = 0

tan (x) = 1087

- 3 sin (3 x) = 1

What is the general solution for 12cos(pi/3 x)+8=0 ?
The general solution for 12cos(pi/3 x)+8=0 is x=(3*2.30052…)/pi+6n,x=-(3*2.30052…)/pi+6n