SOLUTION: I am having real trouble grasping the concepts. Topic: Solving Trigonometric Equations Q: Find all solutions of {{{ sin( 2x ) = -sqrt( 3 )/2 }}} in the interval [0,2pi) Answe

SOLUTION: I am having real trouble grasping the concepts. Topic: Solving Trigonometric Equations Q: Find all solutions of {{{ sin( 2x ) = -sqrt( 3 )/2 }}} in the interval [0,2pi) Answe

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Question 768031: I am having real trouble grasping the concepts.
Topic: Solving Trigonometric Equations
Q:
Find all solutions of in the interval [0,2pi)
Answer Choices:
1. None of these
2. , , ,
3. , , ,
4. , , ,
5. , , ,
Please note: I am only showing ans choices as a frame of reference; I'm more interested in a detailed review of how to work the problem. Also, do I need to draw a unit circle?
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Find the two points on the unit circle illustrated where the

-coordinate is equal to

.

Now,

has to be in the interval [

), but that means

is in the interval [

). Hence the two points you found on the circle are actually 4 possibilities for the value of

, namely

. Divide each possibility for

by 2, and you will have 4 numbers that match one of your answer choices.

John

Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it

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