Trigonometry Examples

$\tan (x)$ , $\cot (x) = \frac{1}{2}$

Step 1

Use the definition of cotangent to find the known sides of the unit circle right triangle. The quadrant determines the sign on each of the values.

$\cot (x) = \frac{adjacent}{opposite}$

Step 2

Find the hypotenuse of the unit circle triangle. Since the opposite and adjacent sides are known, use the Pythagorean theorem to find the remaining side.

$Hypotenuse = \sqrt{{opposite}^{2} + {adjacent}^{2}}$

Step 3

Replace the known values in the equation.

$Hypotenuse = \sqrt{{(2)}^{2} + {(1)}^{2}}$

Step 4

Simplify inside the radical.

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Step 4.1

Raise $2$ to the power of $2$ .

Hypotenuse $= \sqrt{4 + {(1)}^{2}}$

Step 4.2

One to any power is one.

Hypotenuse $= \sqrt{4 + 1}$

Step 4.3

Add $4$ and $1$ .

Hypotenuse $= \sqrt{5}$

Step 5

Use the definition of tangent to find the value of $\tan (x)$ .

$\tan (x) = \frac{opposite}{adjacent}$

Step 6

Substitute in the known values.

$\tan (x) = \frac{2}{1}$

Step 7

Divide $2$ by $1$ .

$\tan (x) = 2$