x is an acuate. Find the value of x in degrees cos⁡(x)=33 x=?

Question

x is an acuate. Find the value of x in degrees  cos⁡(x)=33  x=?

Matthew Rodriguez · Accepted Answer

Step 1  Given  ⇒cot⁡(x)=33  ⇒cot⁡(x)=13  ⇒x=cot−1(13}  arrwox=60∘

Edward Patten · Accepted Answer

Step 1
Take the inverse cotangent of both sides of the equation to extract x from inside the cotangent.

x = a r o t (\frac{\sqrt{3}}{3})

The exact value of

a r o t (\frac{\sqrt{3}}{3})

is

\frac{π}{3}

x = \frac{π}{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 = π + \frac{π}{3}

Simplify

π + \frac{π}{3}

To write

\frac{π}{1}

as a fraction with a common denominator, multiply by

\frac{3}{3}

x = \frac{π}{1} \times \frac{3}{3} + \frac{π}{3}

Write each expression with a common denominator of 3, by multiplying each by an appropriate factor of 1.
Combine.

x = \frac{π \times 3}{1 \times 3} + \frac{π}{3}

Multiply 3 by 1

x = \frac{π \times 3}{3} + \frac{π}{3}

Combine the numerators over the common denominator.

x = \frac{π \times 3 + π}{3}

Simplify the numerator.
Move 3 to the left of

π

x = \frac{3 \times π + π}{3}

Add

3 π

and

π

x = \frac{4 π}{3}

Find the period
The period of the function can be calculated using

\frac{π}{| b |}

Replace b with 1 in the formula for period.

\frac{π}{| 1 |}

Solve the equation.
The absolute value is the distance between a number and zero. The distance between 0 and 1 is 1

\frac{π}{1}

Divide

π

by 1

π

The period of the

\cot (x)

function is

π

so values will repeat every

π

radians in both directions

x = \frac{π}{3} + π n

\frac{4 π}{3} + π n

for any integer n
Consolidate the answers.

x = \frac{π}{3} + π n

for any integer n

x is an acuate. Find the value of x in