Question 963195
Find all solutions of the given trigonometric equation if θ represents an angle measured in degrees.
<pre>
{{{9sqrt(3)sin(theta)}}}{{{""=""}}}{{{9cos(theta)}}}

Divide both sides by 9

{{{sqrt(3)sin(theta)}}}{{{""=""}}}{{{cos(theta)}}}

Divide both sides by {{{sin(theta)}}}

{{{sqrt(3)}}}{{{""=""}}}{{{cos(theta)/sin(theta)}}}

Use the identity {{{cos(theta)/sin(theta)=cot(theta)}}}

{{sqrt(3)}}}{{{""=""}}}{{{cot(theta)}}}

Since cot(30°) = &#8730;3

The basic solution is 30°.

The cotangent is positive in the 1st and 3rd, so 30°+180° = 210°
is also a solution:

Solutions between 0° and 360° are 30° and 210° 

All solutions are given by 30°+180°n where n is any integer.

Edwin</pre>