Find the solution set of the given equation for 0 ≤ x ≤ 2π.

3cotx = sqrt3

Step-by-step explanation:

Answer:

x

=

π

6

+

n

2

π

,

7

π

6

+

n

2

π

, where n is an integer

Explanation:

Start with:

cot

x

-

√

3

=

0

cot

x

=

√

3

This means that:

cos

x

sin

x

=

√

3

1

So the adjacent is length

√

3

and the opposite is length 1. This set us up for the 30/60/90 triangle and the angle we're looking at is the

30

o

or

π

6

one.

So now the question is which quadrants are we looking at. Cotangent is positive in Q1 and Q3. The angles we're looking at, then, are

π

6

and

π

+

π

6

=

7

π

6

.

This question does not limit our answer to any particular domain, and so we need the general solution, which is:

x

=

π

6

+

n

2

π

,

7

π

6

+

n

2

π

, where n is an integer