# Thread: I am confused on this problem?

1. ## I am confused on this problem?

Where did I go wrong on this problem,
Find the exact value of the expression cos^-1[cos(4PI/3)]

cos of 4PI/3 =-1/2
cos^-1 of (-1/2)= 2PI/3 or 2.094395102

2. Originally Posted by cross1933
Where did I go wrong on this problem,
Find the exact value of the expression cos^-1[cos(4PI/3)]

cos of 4PI/3 =-1/2
cos^-1 of (-1/2)= 2PI/3 or 2.094395102
who said it was wrong?

$\cos^{-1}\left[\cos\left(\frac{4\pi}{3}\right)\right] = \cos^{-1}\left(-\frac{1}{2}\right) = \frac{2\pi}{3}$

because ... the range of the inverse cosine function is $0 \leq y \leq \pi$

3. Originally Posted by skeeter
who said it was wrong?

$\cos^{-1}\left[\cos\left(\frac{4\pi}{3}\right)\right] = \cos^{-1}\left(-\frac{1}{2}\right) = \frac{2\pi}{3}$

because ... the range of the inverse cosine function is $0 \leq y \leq \pi$
$2PI/3$ is not one of the answer choices, that is what is confusing me.

4. Originally Posted by stapel
Domain 1,-1
Range 0, $PI$

5. Originally Posted by cross1933
$2PI/3$ is not one of the answer choices, that is what is confusing me.
don't know what to tell you ... but, I know my solution is correct.

6. Originally Posted by skeeter
don't know what to tell you ... but, I know my solution is correct.
Not sure what I will do, maybe I will email one of the class members.

Thanks

7. for the record, what are the answer "choices" ?

8. Originally Posted by skeeter
for the record, what are the answer "choices" ?
1/2
-1/2
$pi/3$
$4pi/3$

9. Originally Posted by cross1933
1/2
-1/2
$pi/3$
$4pi/3$
None of those options are correct. The answer given by you and skeeter is the correct answer.

10. Is it possible the cos^-1 and the cos cancel leaving the answer as $4PI/3$?

11. Originally Posted by cross1933
Is it possible the cos^-1 and the cos cancel leaving the answer as $4PI/3$?
You know that $\frac{4 \pi}{3}$ does not lie in the range of $\cos^{-1}$, so it cannot be the correct answer. (However, whoever wrote the question might not realise this .....)

12. Originally Posted by mr fantastic
You know that $\frac{4 \pi}{3}$ does not lie in the range of $\cos^{-1}$, so it cannot be the correct answer. (However, whoever wrote the question might not realise this .....)
That is true, still hoping I overlooked something simple. The author of the question may not be aware of this?