Solve for C in Degrees cos(C)=0.0698

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Trigonometry

$\cos (C) = 0.0698$

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

$C = \arccos (0.0698)$

Simplify the right side.

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Evaluate $\arccos (0.0698)$ .

$C = 85.99750003$

The cosine function is positive in the first and fourth quadrants. To find the second solution, subtract the reference angle from $360$ to find the solution in the fourth quadrant.

$C = 360 - 85.99750003$

Subtract $85.99750003$ from $360$ .

$C = 274.00249996$

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

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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 $\cos (C)$ function is $360$ so values will repeat every $360$ degrees in both directions.

$C = 85.99750003 + 360 n, 274.00249996 + 360 n$ , for any integer $n$

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