Precalculus Examples

$\sin (A) = 23 \cdot \frac{\sin (28)}{20}$

Step 1

Simplify $23 \cdot \frac{\sin (28)}{20}$ .

Tap for more steps...

Step 1.1

Evaluate $\sin (28)$ .

$\sin (A) = 23 \cdot \frac{0.46947156}{20}$

Step 1.2

Divide $0.46947156$ by $20$ .

$\sin (A) = 23 \cdot 0.02347357$

Step 1.3

Multiply $23$ by $0.02347357$ .

$\sin (A) = 0.53989229$

Step 2

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

$A = \arcsin (0.53989229)$

Step 3

Simplify the right side.

Tap for more steps...

Step 3.1

Evaluate $\arcsin (0.53989229)$ .

$A = 32.67630735$

Step 4

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.

$A = 180 - 32.67630735$

Step 5

Subtract $32.67630735$ from $180$ .

$A = 147.32369264$

Step 6

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

Tap for more steps...

Step 6.1

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

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

Step 6.2

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

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

Step 6.3

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

$\frac{360}{1}$

Step 6.4

Divide $360$ by $1$ .

$360$

Step 7

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

$A = 32.67630735 + 360 n, 147.32369264 + 360 n$ , for any integer $n$