Trigonometry Examples

$\frac{\cos (\frac{7 π}{6})}{\sin (\frac{7 π}{6})}$

Step 1

Simplify the numerator.

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Step 1.1

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because cosine is negative in the third quadrant.

$\frac{- \cos (\frac{π}{6})}{\sin (\frac{7 π}{6})}$

Step 1.2

The exact value of $\cos (\frac{π}{6})$ is $\frac{\sqrt{3}}{2}$ .

$\frac{- \frac{\sqrt{3}}{2}}{\sin (\frac{7 π}{6})}$

Step 2

Simplify the denominator.

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Step 2.1

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because sine is negative in the third quadrant.

$\frac{- \frac{\sqrt{3}}{2}}{- \sin (\frac{π}{6})}$

Step 2.2

The exact value of $\sin (\frac{π}{6})$ is $\frac{1}{2}$ .

$\frac{- \frac{\sqrt{3}}{2}}{- \frac{1}{2}}$

Step 3

Dividing two negative values results in a positive value.

$\frac{\frac{\sqrt{3}}{2}}{\frac{1}{2}}$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$\frac{\sqrt{3}}{2} \cdot 2$

Step 5

Cancel the common factor of $2$ .

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Step 5.1

Cancel the common factor.

$\frac{\sqrt{3}}{2} \cdot 2$

Step 5.2

Rewrite the expression.

$\sqrt{3}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\sqrt{3}$

Decimal Form:

$1.73205080 \dots$