Question

Solve 3cot (2x) =- Route3 for x, 0 = x < 360

Answer 1

Answer:

x=60,150,240,330

Step-by-step explanation:

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

$\cot(2x) = \frac{ - \sqrt{3} }{3}$

Take the arc cot of both sides

$\cot {}^{ - 1} ( \cot(2x) ) = \cot {}^{ - 1} ( \frac{ - \sqrt{3} }{3} )$

$2x = 120$

Remember cotangent has a period of 180 degrees

$2x = 120 + 90(n)$

where n is 0, 1,2,3,4,5.....

Isolate x.

$x = 60 + 90(n)$

where n is 0, 1,2,3,4,5,6.

Keep plugging in integers as long they are in the interval [0,360].

We get

60,150,240,330.