# Thread: Probably a stupid question...

1. ## Probably a stupid question...

So by the trigonometric identities, $\sec \theta = \frac {1} {\cos \theta}$, but according to my calculator, $\sec 0 = 1.57$, and $\cos 0 = 1$. how can this be, seeing as $\frac {1} {1} = 1.57$ isnt true??

2. Originally Posted by Chokfull
So by the trigonometric identities, $\sec \theta = \frac {1} {\cos \theta}$, but according to my calculator, $\sec 0 = 1.57$, and $\cos 0 = 1$. how can this be, seeing as $\frac {1} {1} = 1.57$ isnt true??
When you calculated $Sec(0)$, you didn't happen to find $Cos^{-1}(0)$ by any chance in radian mode?

$Cos^{-1}\theta$ and $\frac{1}{Cos\theta}$ are different.

3. I think Archie nailed it, also showing at the same time the advantage and disadvantage of the calculator/computer. Interesting how the English language can be so subtle and so frustrating at times: "The inverse function" and the inverse OF a function."

4. OK yes i did find $\cos ^{-1} (0)$ on my calculator, because my calculator does not have a secant key. I even searched through all its functions and didn't find it. So I now have 2 more questions:

(1) how do you find cosecant, secant, and cotangent on a TI-85 graphing calculator, and

(2) why are $\frac {1} {\cos 0}$ and $\cos ^{-1}$ different?

5. Originally Posted by Chokfull
OK yes i did find $\cos ^{-1} (0)$ on my calculator, because my calculator does not have a secant key. I even searched through all its functions and didn't find it. So I now have 2 more questions:

(1) how do you find cosecant, secant, and cotangent on a TI-85 graphing calculator, and

(2) why are $\frac {1} {\cos 0}$ and $\cos ^{-1}$ different?
1. You calculate the sine, cosine, and tangent functions (respectively) and then calculate the multiplicative inverse.

2. $\frac {1} {\cos x} = \sec x$ but

$\cos ^{-1} (x) = \arccos x$, which is the inverse of the cosine function. It tells you the angle that would produce a cosine of x.