Solve for C in Degrees 12sin(C)+6=5sin(C)+6

Solve Math

Trigonometry

$12 \sin (C) + 6 = 5 \sin (C) + 6$

Move all terms containing $\sin (C)$ to the left side of the equation.

Tap for more steps...

Subtract $5 \sin (C)$ from both sides of the equation.

$12 \sin (C) + 6 - 5 \sin (C) = 6$

Subtract $5 \sin (C)$ from $12 \sin (C)$ .

$7 \sin (C) + 6 = 6$

Move all terms not containing $\sin (C)$ to the right side of the equation.

Tap for more steps...

Subtract $6$ from both sides of the equation.

$7 \sin (C) = 6 - 6$

Subtract $6$ from $6$ .

$7 \sin (C) = 0$

Divide each term in $7 \sin (C) = 0$ by $7$ and simplify.

Tap for more steps...

Divide each term in $7 \sin (C) = 0$ by $7$ .

$\frac{7 \sin (C)}{7} = \frac{0}{7}$

Simplify the left side.

Tap for more steps...

Cancel the common factor of $7$ .

Tap for more steps...

Cancel the common factor.

$\frac{7 \sin (C)}{7} = \frac{0}{7}$

Divide $\sin (C)$ by $1$ .

$\sin (C) = \frac{0}{7}$

Simplify the right side.

Tap for more steps...

Divide $0$ by $7$ .

$\sin (C) = 0$

Take the inverse sine of both sides of the equation to extract $C$ from inside the sine.

$C = \arcsin (0)$

Simplify the right side.

Tap for more steps...

The exact value of $\arcsin (0)$ is $0$ .

$C = 0$

The sine function is positive in the first and second quadrants. To find the second solution, subtract the reference angle from $180$ to find the solution in the second quadrant.

$C = 180 - 0$

Subtract $0$ from $180$ .

$C = 180$

Find the period of $\sin (C)$ .

Tap for more steps...

The period of the function can be calculated using $\frac{360}{| b |}$ .

$\frac{360}{| b |}$

Replace $b$ with $1$ in the formula for period.

$\frac{360}{| 1 |}$

The absolute value is the distance between a number and zero. The distance between $0$ and $1$ is $1$ .

$\frac{360}{1}$

Divide $360$ by $1$ .

$360$

The period of the $\sin (C)$ function is $360$ so values will repeat every $360$ degrees in both directions.

$C = 360 n, 180 + 360 n$ , for any integer $n$

Consolidate the answers.

$C = 180 n$ , for any integer $n$

Do you know how to Solve for C in Degrees 12sin(C)+6=5sin(C)+6? If not, you can write to our math experts in our application. The best solution for your task you can find above on this page.