The Science That Draws Necessary Conclusions

There are six trigonometric functions. The two most important ones are sine and cosine. The others can be derived from these two functions. The trigonometric functions are based on the ratios between sides that exist in right triangles.

Sine is the ratio of the side opposite of to the hypotenuse. Therefore, . Cosine is the ratio of the side adjacent to to the hypotenuse. Therefore, . A common mnemonic device to remember which funtion refers to which rations is SOH-CAH-TOA. SOH means ; COS means . TOA is for the function tangent. For now just know TOA stands for . Sine and cosine are cofunctions. That means that as well as .

The unit circle is another way to look at sine and cosine. Any angle passes through one point on the unit circle. The point the angle passes through is . Remember that sine and cosine functions both equal the length of a side over the hypotenuse. The length of the hypotenuse of the triangle formed from the angle will always be one in the unit circle. The side opposite of the angle is the same the y-coordinate of the point and the side adjacent is the same as the x-coordinate.

Sine and cosine are also related to the x and y coordinates where an angle intersects a circle concentric with the unit circle. The difference is that the hypotenuse is no longer equal to one. Instead, it is the radius of the circle. Therefore, and .

Next to be discussed are the remaining four trigonometric functions. They should be fairly simple to learn if sine and cosine is easy. The animation above shows the graph of . It will be a topic of later posts.