Question

I don't know where to start on this question.
\[2 \sin \theta - \cos \theta = 0\]
for
\[0 \le \theta < 360 degrees \]

Answer 1

Consider: \[
\begin{split}
2\sin(θ)−\cos(θ)=0 &\implies 2\sin(θ)=\cos(θ) \\
&\implies 2\tan(\theta) = 1 \\
&\implies \tan(\theta) = \frac{1}{2}
\end{split}
\]

Answer 2

@Pianoman1996j what kind of angle do you think this would be?

Answer 3

I am not sure. My teacher gave me the answers of 26.6 deg and 206.6 deg.
How do you get these answers?

Answer 4

@Pianoman1996j Are you allowed to use a calculator with arctan function?

Answer 5

Because in degree mode arctan ( 1 / 2 ) approx 26.6 degrees

Answer 6

There is also the unit circle which can be helpful in some cases.

Answer 7

@wio I am not allowed to use a calculator at all.

Answer 8

Do you know calculus?

Answer 9

The thing is, 26.6 is an obscure angle.
I can understand expecting you to memorize 30, 45, 60, 90, etc
But 26.6?

Answer 10

This is a practice problem for my pre-calc mid term coming up in 2 weeks. My teacher VERY RARELY lets us use calculators. But it does seem (by the answers he gave us) that I would have to on this one.

Answer 11

I think that all which is reasonable to ask of you is to be able to do the algebra I showed you and to set up your triangle like I did.

Answer 12

Thanks. I agree. I just hope my teacher does too. :)

Answer 13

The reason why 206.6 is also a solution is because:

-1 / -2 is also equal to 1/2 and it is within the 360 range