SOLUTION: Find all solutions of the given trigonometric equation if θ represents an angle measured in degrees. 9(squareroot of 3) sin θ = 9 cos θ

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Question 963195: Find all solutions of the given trigonometric equation if θ represents an angle measured in degrees.
9(squareroot of 3) sin θ = 9 cos θ
Answer by Edwin McCravy(20062) About Me  (Show Source):
You can put this solution on YOUR website!
Find all solutions of the given trigonometric equation if θ represents an angle measured in degrees.
9sqrt%283%29sin%28theta%29%22%22=%22%229cos%28theta%29

Divide both sides by 9

sqrt%283%29sin%28theta%29%22%22=%22%22cos%28theta%29

Divide both sides by sin%28theta%29

sqrt%283%29%22%22=%22%22cos%28theta%29%2Fsin%28theta%29

Use the identity cos%28theta%29%2Fsin%28theta%29=cot%28theta%29

{{sqrt(3)}}}%22%22=%22%22cot%28theta%29

Since cot(30°) = √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