Trigonometry Examples

sin (x) cos (x) = \sqrt{\frac{3}{4}}

$\sin (x) \cos (x) = \sqrt{\frac{3}{4}}$

Step 1

Multiply each term in

$\sin (x) \cos (x) = \sqrt{\frac{3}{4}}$ by

$2$ to eliminate the fractions.

Tap for more steps...

Step 1.1

Multiply each term in

$\sin (x) \cos (x) = \sqrt{\frac{3}{4}}$ by

$2$ .

$\sin (x) \cos (x) \cdot 2 = \sqrt{\frac{3}{4}} \cdot 2$

Step 1.2

Simplify the left side.

Tap for more steps...

Step 1.2.1

Reorder

$\sin (x) \cos (x)$ and

$2$ .

$2 \cdot (\sin (x) \cos (x)) = \sqrt{\frac{3}{4}} \cdot 2$

Step 1.2.2

Apply the sine double-angle identity.

$\sin (2 x) = \sqrt{\frac{3}{4}} \cdot 2$

Step 1.3

Simplify the right side.

Tap for more steps...

Step 1.3.1

Rewrite

$\sqrt{\frac{3}{4}}$ as

$\frac{\sqrt{3}}{\sqrt{4}}$ .

$\sin (2 x) = \frac{\sqrt{3}}{\sqrt{4}} \cdot 2$

Step 1.3.2

Simplify the denominator.

Tap for more steps...

Step 1.3.2.1

Rewrite

$4$ as

$2^{2}$ .

$\sin (2 x) = \frac{\sqrt{3}}{\sqrt{2^{2}}} \cdot 2$

Step 1.3.2.2

Pull terms out from under the radical, assuming positive real numbers.

$\sin (2 x) = \frac{\sqrt{3}}{2} \cdot 2$

Step 1.3.3

Cancel the common factor of

$2$ .

Tap for more steps...

Step 1.3.3.1

Cancel the common factor.

$\sin (2 x) = \frac{\sqrt{3}}{2} \cdot 2$

Step 1.3.3.2

Rewrite the expression.

$\sin (2 x) = \sqrt{3}$

Step 2

The range of sine is

$- 1 \leq y \leq 1$ . Since

$\sqrt{3}$ does not fall in this range, there is no solution.

No solution