Trigonometry Examples

$\sin (x) = \sin (50)$

Step 1

For the two functions to be equal, the arguments of each must be equal.

$x = 50$

Step 2

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.

$x = 180 - 50$

Step 3

Subtract $50$ from $180$ .

$x = 130$

Step 4

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

Tap for more steps...

Step 4.1

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

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

Step 4.2

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

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

Step 4.3

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

$\frac{360}{1}$

Step 4.4

Divide $360$ by $1$ .

$360$

Step 5

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

$x = 50 + 360 n, 130 + 360 n$ , for any integer $n$