# 微积分网课代修|微分学代写Differential calculus代考|MATH272 The trigonometric functions

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## 微积分网课代修|微分学代写Differential calculus代考|The trigonometric functions

Let’s review what we know about these functions (Volume 1, Chapter 1PC-4).
One encounters numerous examples of periodic phenomena. The simplest case is that of a quantity that changes but then comes back to change again in the same manner:

Functions with this behavior are called persodic.

## 微积分网课代修|微分学代写Differential calculus代考|periodic behavior

The simplest periodic behavior is oscillation of an object on a spring or a string of a musical instrument:
A more complex example is the trip of the moon around the sun.

Suppose we have a right triangle with sides $a, b, c$, with $c$ being the longest one facing the right angle. If $\alpha$ is the angle adjacent to side $a$, then we define the cosine and the sine of this angle as follows:
\begin{aligned} \cos \alpha &=\frac{a}{c} \ \sin \alpha &=\frac{b}{c} \ \tan \alpha &=\frac{b}{a}=\frac{\sin \alpha}{\cos \alpha} \end{aligned}
The importance of the tangent is seen in this formula:
$$\tan \alpha=\frac{b}{a}=\frac{\text { rise }}{\text { run }}=\text { slope of the hy potenuse } c,$$

## 微积分网课代修|微分学代写Differential calculus代考|periodic behavior

$$\cos \alpha=\frac{a}{c} \sin \alpha=\frac{b}{c} \tan \alpha=\frac{b}{a}=\frac{\sin \alpha}{\cos \alpha}$$

$$\tan \alpha=\frac{b}{a}=\frac{\text { rise }}{\text { run }}=\text { slope of the hy potenuse } c$$