Trigonometry Examples

$\sin (y) = \frac{150 \sin (150)}{280}$

Step 1

Simplify $\frac{150 \sin (150)}{280}$ .

Tap for more steps...

Step 1.1

Cancel the common factor of $150$ and $280$ .

Tap for more steps...

Step 1.1.1

Factor $10$ out of $150 \sin (150)$ .

$\sin (y) = \frac{10 (15 \sin (150))}{280}$

Step 1.1.2

Cancel the common factors.

Tap for more steps...

Step 1.1.2.1

Factor $10$ out of $280$ .

$\sin (y) = \frac{10 (15 \sin (150))}{10 (28)}$

Step 1.1.2.2

Cancel the common factor.

$\sin (y) = \frac{10 (15 \sin (150))}{10 \cdot 28}$

Step 1.1.2.3

Rewrite the expression.

$\sin (y) = \frac{15 \sin (150)}{28}$

Step 1.2

Simplify the numerator.

Tap for more steps...

Step 1.2.1

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant.

$\sin (y) = \frac{15 \sin (30)}{28}$

Step 1.2.2

The exact value of $\sin (30)$ is $\frac{1}{2}$ .

$\sin (y) = \frac{15 (\frac{1}{2})}{28}$

Step 1.3

Combine $15$ and $\frac{1}{2}$ .

$\sin (y) = \frac{\frac{15}{2}}{28}$

Step 1.4

Multiply the numerator by the reciprocal of the denominator.

$\sin (y) = \frac{15}{2} \cdot \frac{1}{28}$

Step 1.5

Multiply $\frac{15}{2} \cdot \frac{1}{28}$ .

Tap for more steps...

Step 1.5.1

Multiply $\frac{15}{2}$ by $\frac{1}{28}$ .

$\sin (y) = \frac{15}{2 \cdot 28}$

Step 1.5.2

Multiply $2$ by $28$ .

$\sin (y) = \frac{15}{56}$

Step 2

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

$y = \arcsin (\frac{15}{56})$

Step 3

Simplify the right side.

Tap for more steps...

Step 3.1

Evaluate $\arcsin (\frac{15}{56})$ .

$y = 15.53679406$

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.

$y = 180 - 15.53679406$

Step 5

Subtract $15.53679406$ from $180$ .

$y = 164.46320593$

Step 6

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

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

$y = 15.53679406 + 360 n, 164.46320593 + 360 n$ , for any integer $n$