Trigonometry Examples

$\cot (30) = \cos (x)$

Step 1

Rewrite the equation as $\cos (x) = \cot (30)$ .

$\cos (x) = \cot (30)$

Step 2

Simplify the expression using the $h a l f - a n g l e$ formula.

$\pm \sqrt{\frac{1 + \cos (2 x)}{2}} = \cot (30)$

Step 3

Remove the $\pm$ from both sides of the equation.

$\sqrt{\frac{1 + \cos (2 x)}{2}} = \cot (30)$

Step 4

Since the square roots of each expression are equal, the expression inside the square root must also be equal.

$\frac{1 + \cos (2 x)}{2} = \cot (30)$

Step 5

Multiply both sides of the equation by $2$ .

$2 \frac{1 + \cos (2 x)}{2} = 2 \cot (30)$

Step 6

Simplify both sides of the equation.

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Step 6.1

Simplify the left side.

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Step 6.1.1

Cancel the common factor of $2$ .

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Step 6.1.1.1

Cancel the common factor.

$2 \frac{1 + \cos (2 x)}{2} = 2 \cot (30)$

Step 6.1.1.2

Rewrite the expression.

$1 + \cos (2 x) = 2 \cot (30)$

Step 6.2

Simplify the right side.

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Step 6.2.1

The exact value of $\cot (30)$ is $\sqrt{3}$ .

$1 + \cos (2 x) = 2 \sqrt{3}$

Step 7

Subtract $1$ from both sides of the equation.

$\cos (2 x) = 2 \sqrt{3} - 1$

Step 8

Convert the right side of the equation to its decimal equivalent.

$\cos (2 x) = 2.46410161$

Step 9

The range of cosine is $- 1 \leq y \leq 1$ . Since $2.46410161$ does not fall in this range, there is no solution.

No solution