Can someone tell my what cos, sin and tan actually measure?
In: Mathematics
It’s a ratio between the sides of a right triangle. Take a triangle with one 90 degree angle and choose one of the other two angles to start with. This will be our starting angle. Now, because all triangles have angles which add to 180 degrees, the sum of the other two angles must also add up to 90.
From our starting angle, we define 3 ratios: Sine, Cosine, and Tangent. Let’s name the 3 sides of the triangle. The **hypotenuse** is the longest side of the triangle, which is the side that is opposite the 90 degree angle. The remaining side closest to our starting angle is called **adjacent**. The third side, opposite our starting angle is called **opposite**.
**Sine** is defined as the ratio of the **opposite** divided by the **hypotenuse**.
**Cosine** is defined as the ratio of the **adjacent** divided by the **hypotenuse**.
**Tangent** is defined as the ratio of the **opposite** divided by the **adjacent**.
S=O/H
C=A/H
T=O/A
If you define the length of the hypotenuse to be one unit, Sine measures the height of the opposite side, while cosine measures the length of the adjacent side.
Using this **Unit Circle**, you can find the *y* and *x* coordinates on a graph of any point on that circle if you know the angle of the triangle, or if you know one of the two lengths.
Conversely, if you know the length of any two sides of the triangle, given that one angle is a 90 degree angle, you can easily find the angles using these functions, and compute the length of the third side.
This is basically all of trigonometry condensed. It takes a while to get the hang of it all.
Trigonometry is basically defining triangles based on circles, and defining circles based on triangles. If you have a little information, you can deduce the rest of the information, due to this fundamental fact that triangles always add up to 180 degrees. It’s the Pythagorean theorem with extra steps.
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