Trigonometry Examples

$\cot (x) = 2$

Step 1

Take the inverse cotangent of both sides of the equation to extract

$x$ from inside the cotangent.

$x = arccot (2)$

Step 2

Simplify the right side.

Tap for more steps...

Step 2.1

Evaluate

$arccot (2)$ .

$x = 0.4636476$

Step 3

The cotangent function is positive in the first and third quadrants. To find the second solution, add the reference angle from

$π$ to find the solution in the fourth quadrant.

$x = (3.14159265) + 0.4636476$

Step 4

Solve for

$x$ .

Tap for more steps...

Step 4.1

Remove parentheses.

$x = 3.14159265 + 0.4636476$

Step 4.2

Remove parentheses.

$x = (3.14159265) + 0.4636476$

Step 4.3

Add

$3.14159265$ and

$0.4636476$ .

$x = 3.60524026$

Step 5

Find the period of

$\cot (x)$ .

Tap for more steps...

Step 5.1

The period of the function can be calculated using

$\frac{π}{| b |}$ .

$\frac{π}{| b |}$

Step 5.2

Replace

$b$ with

$1$ in the formula for period.

$\frac{π}{| 1 |}$

Step 5.3

The absolute value is the distance between a number and zero. The distance between

$0$ and

$1$ is

$1$ .

$\frac{π}{1}$

Step 5.4

Divide

$π$ by

$1$ .

$π$

Step 6

The period of the

$\cot (x)$ function is

$π$ so values will repeat every

$π$ radians in both directions.

$x = 0.4636476 + π n, 3.60524026 + π n$ , for any integer

$n$

Step 7

Consolidate

$0.4636476 + π n$ and

$3.60524026 + π n$ to

$0.4636476 + π n$ .

$x = 0.4636476 + π n$ , for any integer

$n$

$\cot (x) = 2$

(

)

[

]

√



≥















≤



































