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

[jrjack]

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

Homework Statement

$$\cos\theta=\frac{\pi}{2}$$ HINT:The real number $\frac{\pi}{2}$ is not an angle.

Homework Equations

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?

 

[SammyS]

What is an approximate value for π/2 numerically?

 

[jrjack]

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

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

 

[uart]

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

 

[jrjack]

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.

 

[rock.freak667]

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.

You might want to say no real solutions instead though.

 

[jrjack]

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

 

[uart]

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

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.