SOLUTION: Solve the equation on the interval of 0 < theta <2pi sqrt 3 sin theta+cos theta=1

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Question 525245: Solve the equation on the interval of 0 < theta <2pi
sqrt 3 sin theta+cos theta=1
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!






Square both sides:



Use the Pythagorean Identity to replace the in the LHS with



Collect like terms and divide by 2:



Let and make the substitution:



Factor:



Then



or



Substitute back:



Note: and are excluded by your interval statement:



Or:

or

Verify on the unit circle:

Note: is the coordinate on the Unit Circle.

John

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