Representing cos(npi/2) in general form

Thread starter nutcase21
Start date Feb 26, 2012
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In summary, the general form of cos(npi/2) is (-1)^n, where n is an integer. Cos(npi/2) is represented by the x-coordinate of a point on the unit circle at an angle of npi/2 radians from the origin. To find the value of cos(npi/2) for non-integer values of n, one can use trigonometric identities or the double-angle formula. The relationship between cos(npi/2) and sin(npi/2) is that they are complementary functions. Cos(npi/2) can be used in practical applications such as engineering, physics, and astronomy to calculate the amplitude and phase of periodic functions and in signal processing and the analysis of

Feb 26, 2012

nutcase21

hi i am currently trying to solve a Fourier series question and i realize for example cos(npi) can be represented as (-1)ⁿ.

So i was wandering is there anyway to represent cos(npi/2) to a general form too?

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Feb 26, 2012

Office_Shredder

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i suppose something like
(1+(-1)ⁿ)/2*(-1)^n/2

Feb 26, 2012

nutcase21

OIC thnks.

is there any tricks to getting the general form?

1. What is the general form of cos(npi/2)?

The general form of cos(npi/2) is (-1)^n, where n is an integer.

2. How is cos(npi/2) represented on the unit circle?

Cos(npi/2) is represented by the x-coordinate of a point on the unit circle at an angle of npi/2 radians from the origin.

3. How do you find the value of cos(npi/2) for non-integer values of n?

You can use the trigonometric identities to find the value of cos(npi/2) for non-integer values of n. For example, if n is a decimal value, you can use the double-angle formula to express cos(npi/2) in terms of cos(npi/2) and cos(npi/2), which can then be evaluated using a calculator or table.

4. What is the relationship between cos(npi/2) and sin(npi/2)?

The relationship between cos(npi/2) and sin(npi/2) is that they are complementary functions. This means that cos(npi/2) = sin(npi/2 + pi/2) and sin(npi/2) = cos(npi/2 - pi/2). In other words, cos(npi/2) and sin(npi/2) are equal in magnitude but have opposite signs.

5. How can cos(npi/2) be used in practical applications?

Cos(npi/2) can be used in practical applications such as engineering, physics, and astronomy to calculate the amplitude and phase of periodic functions. It is also commonly used in signal processing and in the analysis of oscillations and vibrations.