Trigonometry Examples

$\cos (x) - \frac{\frac{1}{2}}{\cos (x)} = - \frac{1}{2}$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

Separate fractions.

$\cos (x) - (\frac{\frac{1}{2}}{1} \cdot \frac{1}{\cos (x)}) = - \frac{1}{2}$

Step 1.2

Convert from $\frac{1}{\cos (x)}$ to $\sec (x)$ .

$\cos (x) - (\frac{\frac{1}{2}}{1} \sec (x)) = - \frac{1}{2}$

Step 1.3

Divide $\frac{1}{2}$ by $1$ .

$\cos (x) - (\frac{1}{2} \sec (x)) = - \frac{1}{2}$

Step 1.4

Combine $\frac{1}{2}$ and $\sec (x)$ .

$\cos (x) - \frac{\sec (x)}{2} = - \frac{1}{2}$

Step 2

Graph each side of the equation. The solution is the x-value of the point of intersection.

$x = \frac{π}{3} + \frac{2 π n}{3}$ , for any integer $n$

Step 3