How is sin(npi/2) = (-1)^((n-1)/2) for odd n?

Thread starter jaejoon89
Start date Sep 19, 2009

In summary, the value of sin(npi/2) for odd values of n can be calculated using the formula (-1)^((n-1)/2), which is derived from the properties of sine function and the relationship between sine and cosine functions. This formula holds true for odd values of n because npi/2 falls in the second or fourth quadrant of the unit circle, where the sine function is equal to -1 or 1 respectively. It cannot be used for even values of n, and has applications in mathematics, physics, and engineering. There is a mathematical proof for this formula using the properties of sine and cosine functions.

Sep 19, 2009

jaejoon89

I know the MacLaurin series for sin(x) but can't figure out how this reduces to the above (if it does).

Physics news on Phys.org

Sep 19, 2009

JG89

sin(npi/2) is going to be equal to -1 or 1, depending on the value of n, right? So the formula seems plausible. You could prove it through induction.

Last edited: Sep 19, 2009

Sep 19, 2009

jaejoon89

thanks

FAQ: How is sin(npi/2) = (-1)^((n-1)/2) for odd n?

1. How is sin(npi/2) calculated for odd values of n?

The value of sin(npi/2) for odd values of n can be calculated using the formula (-1)^((n-1)/2), where n is the odd number. This formula is derived from the properties of sine function and the relationship between sine and cosine functions.

2. Why is sin(npi/2) equal to (-1)^((n-1)/2) for odd values of n?

This relationship holds true for odd values of n because when n is odd, the value of npi/2 falls in the second or fourth quadrant of the unit circle, where the sine function is equal to -1 or 1 respectively. This property of sine function is reflected in the formula (-1)^((n-1)/2).

3. Can this formula be used for even values of n?

No, this formula is only valid for odd values of n. For even values of n, the value of sin(npi/2) is 0, and does not follow this formula.

4. How can this formula be applied in real-world scenarios?

This formula is commonly used in mathematics and physics to calculate the values of sine function for odd values of n. It also has applications in various engineering fields, such as signal processing, where sine waves are frequently used.

5. Is there a proof for this formula?

Yes, there is a mathematical proof for this formula using the properties of sine and cosine functions, and the relationship between them. This proof can be found in most calculus textbooks or online resources.