# Trigonometry

In calculus, instead of working in degrees which you are probably already familiar with, we work in a different, yet equivalent, angle measurement. The measurements don't change in amount, but they are expressed a little bit differently. For example, the angle opposite to the hypotenuse of a right triangle measures 90 degrees. We need to convert this to radians. To convert any angle in degrees to radians multiply the angle in degrees by
/180. So 90 * /180 = /2. So 90 degrees is /2 radians.

You might be wondering why we work in radians instead of degrees. We are more familiar with degrees, but radians is a more natural way to work with angles. One degree is based on an arbitrary measurement, but radian measure is based on the circumference of a unit circle. A unit circle is a circle with radius equal to 1. The circumference of that circle is 2. So if we travel once around the whole circle, we have travelled 2 radians which is equal to 360 degrees. So when we are talking about a quarter of a circle which is 90 degrees we are multiplying 2 by 1/4 which is /2. Ta Da we have our radian masure. Now you know why we use radians in Calculus.

We will need to know some common ratios of sides of a right triangle.

An easy way to remember them is with acronyms. Sine is opposite over hypotenuse. Making the the word 'soh'. Pronounced like the work 'so' as in 'So what?'. Cosine can be remembered by cah which is may be how someone from England might pronounce 'car.' The tangent equation makes the word Toa. 'My feet are swollen. Please don't step on my toa.' The cosine and sine functions are not a phenomenom limited to mathematics which can be used to model ocean and light waves.

Also there are a number of trigonometric identities. Some of them don't show up too much, but if you are going to remember one, remember this one: