Trigonometry Examples

$\sin (B) = \frac{5 \sin (70)}{7}$

Step 1

Simplify $\frac{5 \sin (70)}{7}$ .

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Step 1.1

Evaluate $\sin (70)$ .

$\sin (B) = \frac{5 \cdot 0.93969262}{7}$

Step 1.2

Multiply $5$ by $0.93969262$ .

$\sin (B) = \frac{4.6984631}{7}$

Step 1.3

Divide $4.6984631$ by $7$ .

$\sin (B) = 0.67120901$

Step 2

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

$B = \arcsin (0.67120901)$

Step 3

Simplify the right side.

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Step 3.1

Evaluate $\arcsin (0.67120901)$ .

$B = 42.16044585$

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.

$B = 180 - 42.16044585$

Step 5

Subtract $42.16044585$ from $180$ .

$B = 137.83955414$

Step 6

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

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

$B = 42.16044585 + 360 n, 137.83955414 + 360 n$ , for any integer $n$