Calculus Examples

$1.57 \sin (33.5) = 1.33 \sin (x)$

Step 1

Rewrite the equation as $1.33 \sin (x) = 1.57 \sin (33.5)$ .

$1.33 \sin (x) = 1.57 \sin (33.5)$

Step 2

Multiply $1.57$ by $\sin (33.5)$ .

$1.33 \sin (x) = 0.86654106$

Step 3

Divide each term in $1.33 \sin (x) = 0.86654106$ by $1.33$ and simplify.

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Step 3.1

Divide each term in $1.33 \sin (x) = 0.86654106$ by $1.33$ .

$\frac{1.33 \sin (x)}{1.33} = \frac{0.86654106}{1.33}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $1.33$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{1.33 \sin (x)}{1.33} = \frac{0.86654106}{1.33}$

Step 3.2.1.2

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

$\sin (x) = \frac{0.86654106}{1.33}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $0.86654106$ by $1.33$ .

$\sin (x) = 0.65153463$

Step 4

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

$x = \arcsin (0.65153463)$

Step 5

Simplify the right side.

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Step 5.1

Evaluate $\arcsin (0.65153463)$ .

$x = 40.65740708$

Step 6

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.

$x = 180 - 40.65740708$

Step 7

Subtract $40.65740708$ from $180$ .

$x = 139.34259291$

Step 8

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

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Step 8.1

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

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

Step 8.2

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

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

Step 8.3

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

$\frac{360}{1}$

Step 8.4

Divide $360$ by $1$ .

$360$

Step 9

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

$x = 40.65740708 + 360 n, 139.34259291 + 360 n$ , for any integer $n$