Finding secant with calculator

[bobsmith76]

Homework Statement

what is sec(pi/4)
what is sec(0)

The Attempt at a Solution

First let me make sure that cos^-1, acos and sec, they are all the same right?

I put in cos^-1(pi/4) in my calculator and the answer I get is .667, which I think is the same as sec (pi/4). The book says the answer is √2

 

[eumyang]

Homework Statement

what is sec(pi/4)
what is sec(0)

The Attempt at a Solution

First let me make sure that cos^-1, acos and sec, they are all the same right?

No! They are not the same. The first two, cos^-1 and acos (do you mean arccosine?) are the inverse cosine functions. Put it simply, if cos(π/6) = √3/2, then cos^-1(√3/2) = π/6.

You are confusing these with secant, which is the reciprocal of cosine. In order to evaluate secant on the calculator, you need to type
1/cos(your angle).

 

[bobsmith76]

But I still don't see why sec(pi/4) is √2, it should be 2/√2 and my book clearly says it's √2

 

[phyzguy]

Since √2 * √2 = 2, then 2/√2 = √2 .

 

[bobsmith76]

That doesn't make sense. cos (pi/4) = √2/2. If you take the inverse, which is the secant, then it's 2/√2, not sqaure root of 2

 

[SammyS]

You could do the following subtraction:

$\displaystyle \sqrt{2}-\frac{2}{\sqrt{2}}$​

The answer is zero.

Or the following multiplication:
$\displaystyle \frac{\sqrt{2}}{1}\cdot\frac{\sqrt{2}}{\sqrt{2}}$

 

[bobsmith76]

Sammy, all that gives 2√2, the book clearly says otherwise

 

[phyzguy]

What we're trying to tell you is that 2/√2 and √2 are just different ways of writing the same number. They are equal. They are the same. You and the book are both right.

 

[SammyS]

Sammy, all that gives 2√2, the book clearly says otherwise

Actually, neither one gives 2√(2) .

$\displaystyle \sqrt{2}-\frac{2}{\sqrt{2}}=\frac{\sqrt{2}\sqrt{2}}{\sqrt{2}}-\frac{2}{\sqrt{2}}=\frac{2}{\sqrt{2}}-\frac{2}{\sqrt{2}}=0$

$\displaystyle \frac{\sqrt{2}}{1}\cdot\frac{\sqrt{2}}{\sqrt{2}}= \frac{\sqrt{2}\sqrt{2}}{\sqrt{2}}=\frac{2}{\sqrt{2}}$

⟵ This is correct !

 

[bobsmith76]

o, don't I feel stupid. thanks