Brief discussion on trigonometric system

High School first introduced "two horns and the cosine of difference, sine, tangent" is in Shanghai Education Press High School first grade second semester textbooks, we through the unit circle in two coordinate points of rotation, constructed a corner. Do not repeat the details.

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We know

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We use such a good nature to calculate

Got a

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The above four formulas are the important basis for us to derive the accumulation and difference. We add the sine of the two angle and the sine of the two angular difference first.

Subtract the sine of the two angles from the sine of the two angle difference and you can get

Of course, these two formulas suffice to illustrate that the first question in this paper is that the product of a sine function and a cosine function is a linear combination that can be equivalent to two sine functions.

Based on this view, we calculate a sine function and a vector inner product of a cosine function.

The sine function is an odd function, so it proves a point:

The arbitrary sine function is orthogonal to any cosine function.

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We have just added the sine of the two horns and the sine of the two angle difference, and now we add the cosine of the two angles to the two angle difference.

We subtract the cosine of the two horns from the Yu Yingsiang of the two-angle difference.

Similarly, we can conclude that any two independent variables are orthogonal to the positive (remainder) chord function.

We calculate the inner product of a sine function of any two independent variables, where

The cosine function is even function, however, so we have proved orthogonal to this conclusion.

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Any two independent variables have different cosine function inner product, where

Similarly.

Brief discussion on trigonometric system