Finding secant with calculator

In summary, we are discussing the difference between inverse cosine functions and secant. We clarify that secant is the reciprocal of cosine and provide an example of how to evaluate it on a calculator. We also explain that 2/√2 and √2 are equivalent, leading to a clear understanding of the given problem.
  • #1
bobsmith76
336
0

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
 
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  • #2
bobsmith76 said:

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).
 
  • #3
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
 
  • #4
Since √2 * √2 = 2, then 2/√2 = √2 .
 
  • #5
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
 
  • #6
You could do the following subtraction:
[itex]\displaystyle \sqrt{2}-\frac{2}{\sqrt{2}}[/itex]​
The answer is zero.

Or the following multiplication:
[itex]\displaystyle \frac{\sqrt{2}}{1}\cdot\frac{\sqrt{2}}{\sqrt{2}}[/itex]
 
  • #7
Sammy, all that gives 2√2, the book clearly says otherwise

Screenshot2012-02-02at53653PM.png
 
  • #8
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.
 
  • #9
bobsmith76 said:
Sammy, all that gives 2√2, the book clearly says otherwise
Actually, neither one gives 2√(2) .

[itex]\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[/itex]

[itex]\displaystyle \frac{\sqrt{2}}{1}\cdot\frac{\sqrt{2}}{\sqrt{2}}= \frac{\sqrt{2}\sqrt{2}}{\sqrt{2}}=\frac{2}{\sqrt{2}}[/itex]

Screenshot2012-02-02at53653PM.png
⟵ This is correct !
 
  • #10
o, don't I feel stupid. thanks
 

1. What is a secant on a calculator?

A secant on a calculator is a mathematical function that calculates the ratio of the length of the hypotenuse to the length of the adjacent side in a right triangle. It is commonly used in trigonometry to find the value of an angle or the length of a side.

2. How do I find the secant on a calculator?

To find the secant on a calculator, you will need to use the "cos" function. First, input the angle in degrees or radians, depending on the calculator's settings. Then, press the "cos" button, and the resulting value will be the secant of that angle.

3. Can I use a scientific calculator to find the secant?

Yes, most scientific calculators have a "cos" function that can be used to find the secant. Some calculators may also have a dedicated "sec" button that can be used directly to find the secant.

4. What if my calculator does not have a "cos" or "sec" button?

If your calculator does not have a "cos" or "sec" button, you can still find the secant by using the inverse cosine function. This function is usually denoted as "cos⁻¹" or "arccos" on most calculators. Input the angle in degrees or radians, press the inverse cosine button, and the resulting value will be the secant.

5. Can I use a calculator to find the secant of any angle?

Yes, you can use a calculator to find the secant of any angle. However, some calculators may have limitations on the range of angles they can calculate. Make sure to check your calculator's instructions or manual to ensure the angle you are trying to find the secant of is within its range of capabilities.

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