Dewie B.

asked • 03/17/20

Solve equation for unknown angle

I've been solving equations like 2(sinx)^2+sinx=1 that can be done using factoring and that's not too hard. But now I have an equation sinx-cosx=1/2 and nothing is squared so I don't know how to even start. Help please.

Dewie B.

I have to give all answers between 0 and 2pi and answers must be exact, if that makes any difference.
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03/17/20

Arthur D.

tutor
Did you write the equation wrong ? Should it be cosx-sinx=1/2 ?
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03/17/20

3 Answers By Expert Tutors

By:

Rich G. answered • 03/17/20

Tutor
5.0 (140)

Experienced Pre-Calculus/Trigonometry Tutor

Dewie B.

That's a good try at it. I never would have thought to square both sides. But I tried plugging your answer into the original equation and it didn't work.
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03/17/20

Carmine F.

tutor
I’m sorry! I’ll take a look! It was very late when I was looking at this. I’m guessing it has something to do with the function being non-monotone.
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03/17/20

Carmine F.

tutor
So if you shift the answer I gave you 180 degrees you get a base case solution (in degrees). I’m not sure where the thing breaks down, but I’m guessing that it has to do with the squaring step. At that point it makes the solution equal to the solution to ct-st=1/2. I’ll look further into it, periodic functions are an interesting bunch!
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03/17/20

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