# Cos theta=pi/2 hint pi/2 is not an angle.

1. Jul 24, 2011

### jrjack

cos theta=pi/2....hint pi/2 is not an angle.

1. The problem statement, all variables and given/known data
$$\cos\theta=\frac{\pi}{2}$$ HINT:The real number $\frac{\pi}{2}$ is not an angle.

2. Relevant equations

3. The attempt at a solution

I tried $0=\cos^{-1} \frac{\pi}{2}$, but that equals no solution.
And if $\frac{\pi}{2}$ were an angle the answer would be 0.

Am I solving this correctly?

2. Jul 24, 2011

### SammyS

Staff Emeritus
Re: cos theta=pi/2....hint pi/2 is not an angle.

What is an approximate value for π/2 numerically?

3. Jul 24, 2011

### jrjack

Re: cos theta=pi/2....hint pi/2 is not an angle.

$\pi \approx 3.14$ so $\frac{\pi}{2}\approx 1.57$

and since $\cos\theta=1.57, then...\theta=no solution, because: \cos\theta= -1\leq\theta\geq1$

4. Jul 24, 2011

### uart

Re: cos theta=pi/2....hint pi/2 is not an angle.

Hi jrjack. Are you at all familiar with complex numbers?

5. Jul 24, 2011

### jrjack

Re: cos theta=pi/2....hint pi/2 is not an angle.

I'm not sure, but NO SOLUTION is always one of the possible options.

Please explain further how to use complex numbers in this problem.

6. Jul 24, 2011

### rock.freak667

Re: cos theta=pi/2....hint pi/2 is not an angle.

You might want to say no real solutions instead though.

7. Jul 24, 2011

### jrjack

Re: cos theta=pi/2....hint pi/2 is not an angle.

Of course, No Real Solution. Since we are not dealing with imaginary numbers in this lesson, I think that is appropriate. Thanks.

8. Jul 24, 2011

### uart

Re: cos theta=pi/2....hint pi/2 is not an angle.

Yes that was my point exactly. :)

If you are only dealing with real numbers there is no solution. If you are allowed to use complex numbers (real and imaginary) then there are solutions.