Trigonometry Examples

$\cos (298) = \cos (x)$

Step 1

Rewrite the equation as $\cos (x) = \cos (298)$ .

$\cos (x) = \cos (298)$

Step 2

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

$x = 298$

Step 3

The cosine function is positive in the first and fourth quadrants. To find the second solution, subtract the reference angle from $360$ to find the solution in the fourth quadrant.

$x = 360 - 298$

Step 4

Subtract $298$ from $360$ .

$x = 62$

Step 5

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

Tap for more steps...

Step 5.1

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

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

Step 5.2

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

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

Step 5.3

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

$\frac{360}{1}$

Step 5.4

Divide $360$ by $1$ .

$360$

Step 6

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

$x = 62 + 360 n, 298 + 360 n$ , for any integer $n$