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

Question 525245: Solve the equation on the interval of 0 < theta <2pi
sqrt 3 sin theta+cos theta=1
Answer by solver91311(24713) (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

Substitute back:

Note:

and

are excluded by your interval statement:

Or:

Verify on the unit circle:

Note:

is the

coordinate on the Unit Circle.

John

My calculator said it, I believe it, that settles it

The Out Campaign: Scarlet Letter of Atheism

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