Trigonometry Examples

$\cos (2) x = \frac{\sqrt{2}}{2}$

Step 1

Divide each term in $\cos (2) x = \frac{\sqrt{2}}{2}$ by $\cos (2)$ .

$\frac{\cos (2) x}{\cos (2)} = \frac{\frac{\sqrt{2}}{2}}{\cos (2)}$

Step 2

Simplify the left side.

Tap for more steps...

Step 2.1

Cancel the common factor of $\cos (2)$ .

Tap for more steps...

Step 2.1.1

Cancel the common factor.

$\frac{\cos (2) x}{\cos (2)} = \frac{\frac{\sqrt{2}}{2}}{\cos (2)}$

Step 2.1.2

Divide $x$ by $1$ .

$x = \frac{\frac{\sqrt{2}}{2}}{\cos (2)}$

Step 3

Simplify the right side.

Tap for more steps...

Step 3.1

Separate fractions.

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

Step 3.2

Convert from $\frac{1}{\cos (2)}$ to $\sec (2)$ .

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

Step 3.3

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

$x = \frac{\sqrt{2}}{2} \sec (2)$

Step 3.4

Evaluate $\sec (2)$ .

$x = \frac{\sqrt{2}}{2} \cdot 1.00060954$

Step 3.5

Multiply $\frac{\sqrt{2}}{2} \cdot 1.00060954$ .

Tap for more steps...

Step 3.5.1

Combine $\frac{\sqrt{2}}{2}$ and $1.00060954$ .

$x = \frac{\sqrt{2} \cdot 1.00060954}{2}$

Step 3.5.2

Multiply $\sqrt{2}$ by $1.00060954$ .

$x = \frac{1.41507558}{2}$

Step 3.6

Divide $1.41507558$ by $2$ .

$x = 0.70753779$