How to express cos((n*pi*)/2))

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In summary, the formula for expressing cos((n*pi)/2) is (-1)^n. To find the value of cos((n*pi)/2) for a specific value of n, simply substitute the value of n into the formula (-1)^n. This expression cannot be simplified further and has a range of values between -1 and 1. Cos((n*pi)/2) is related to the unit circle as it represents the x-coordinate of a point on the unit circle, with its value being found by finding the x-coordinate of a point that is n/2 radians counterclockwise from (1,0).
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ETT
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I am doing PDE, heat equation with Homogenous BC's...

I am solving my constant, Bn, but I do not know how to express cos((n*pi*)/2)).
I know that cos(n*pi) is (-1)^n...but what is cos((n*pi*)/2)).


Thank you.
 
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  • #2
Well, it's one of -1, 0, or 1, depending on the value of n.

Make a table with values of n and the corresponding values of cos(n*pi/2), and see if you can discover a pattern.
 

FAQ: How to express cos((n*pi*)/2))

What is the formula for expressing cos((n*pi)/2)?

The formula for expressing cos((n*pi)/2) is: (-1)^n

How do I find the value of cos((n*pi)/2) for a specific value of n?

To find the value of cos((n*pi)/2) for a specific value of n, simply substitute the value of n into the formula (-1)^n. For example, if n=2, then cos((2*pi)/2) = (-1)^2 = 1.

3. Can cos((n*pi)/2) be simplified further?

No, the formula (-1)^n is the simplest expression for cos((n*pi)/2).

4. What is the range of values for cos((n*pi)/2)?

The range of values for cos((n*pi)/2) is between -1 and 1, as (-1)^n can only result in either -1 or 1 for any integer value of n.

5. How is cos((n*pi)/2) related to the unit circle?

Cos((n*pi)/2) is a trigonometric function that represents the x-coordinate of a point on the unit circle. The value of cos((n*pi)/2) for a given value of n can be found by finding the x-coordinate of the point on the unit circle that is n/2 radians (or n*90 degrees) counterclockwise from the point (1,0).

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