Math Doubts. General or Standard form of a Polynomial in One variable. Maths Topics Learn each topic of the mathematics easily with understandable proofs and visual animation graphics. Maths Problems Learn how to solve the maths problems in different methods with understandable steps. This can be challenging, especially if you are not aware of how it is written. This article provides a clear guide on how to write and use SIN squared in excel.
For illustrative purposes, let us consider the following example;. Figure 1: Sine squared in excel. In this example, we have the angle, marked as X. To get the sine squared we simply square the sine. This can be done as shown below;. Note that the results for the sine squared do not have negative. This is because the negatives shall cancel each other during the multiplication to only remain with positives.
Plugging that in, we get:. We rewrite and use integration by parts in its recursive version :. We now rewrite and obtain:. Setting to be a choice of antiderivative so that the above holds without any freely floating constants, we get:.
Using the double angle sine formula , we can verify that this matches with the preceding answer. In the picture below, we depict blue and the function purple. This is the unique antiderivative that takes the value 0 at 0. The other antiderivatives can be obtained by vertically shifting the purple graph:. The black dots correspond to local extreme values for , and the red dots correspond to points of inflection for the antiderivative.
Each black dot is in the same vertical line as a red dot, as we should expect, because points of inflection for the antiderivative correspond to local extreme values for the original function. The part in the antiderivative signifies that the linear part of the antiderivative of has slope , and this is related to the fact that has a mean value of on any interval of length equal to the period.
It is in fact clear that the function is a sinusoidal function about. The mean value of over an interval of length equal to a multiple of the period is. Based on the integration of , we can also integrate the square of any sinusoidal function using the integration of linear transform of function :. We thus see that the mean value of this function is also over any interval of length a multiple of the period. It is possible to antidifferentiate more than once.
The antiderivative is the sum of a polynomial of degree and a trigonometric function with a period of. The power series for is:. We will be focusing on this triangle. In the above image, take a moment to recall what?
It's actually the reference angle, correct? It is one of the most important angles in trigonometry. In the reference angle, what does it mean if the X coordinate equals X?
It means that the length of the X segment is X. In a similar sense, if the Y coordinate is Y, that means the length of the vertical segment of the triangle would be Y. In the above example, there's a point called 3,5.
If we draw a triangle, the 3 depicts the X coordinate. This means that the length of this segment is 3. Now, if the Y coordinate is 5, what does that mean? The length of the vertical segment in the triangle must be five. Going back to the previous unit circle illustration, let's focus on the right-angled triangle and apply the Pythagoras theorem. What is the Pythagoras theorem?
The Pythagoras tells us that X squared plus Y squared equals to the hypotenuse squared. The hypotenuse in this case is one, since we're using a unit circle. So here we have X squared plus Y squared equals one squared. One neat thing about the unit circle is that its X coordinate can also be represented in terms of the angle theta. The X coordinate can be represented as cosine theta, while its Y coordinate can be represented as sine theta.
Keep in mind that this is only for a unit circle.
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