# Question 3bb49

Jan 27, 2018

See below

#### Explanation:

By "symbol functions for trigonometry," I think you meant the trigonometric functions. Here are the 3 basic trig functions:

Sine: $\sin \theta$
Cosine: $\cos \theta$
Tangent: $\tan \theta = \sin \frac{\theta}{\cos} \theta$

And here are the other 3 trig functions (called reciprocal functions) and their definitions:

Cosecant: $\csc \theta = \frac{1}{\sin} \theta$
Secant: $\sec \theta = \frac{1}{\cos} \theta$
Cotangent: $\cot \theta = \frac{1}{\tan} \theta = \frac{1}{\sin \frac{\theta}{\cos} \theta} = \cos \frac{\theta}{\sin} \theta$

Each one also has its own inverse, which takes in the output of its original function and returns what the input would have been. It's written with a $- 1$ exponent like this:

sin^-1(1/2) = 30º = pi/6

cot^-1(1) = 45º = pi/4

You may also see it written as "arc-" and then the function name, for instance:

arcsin(sqrt(3)/2)=60º=pi/3

arctan(sqrt(3))=60º=pi/3#

"Arc-" functions and inverse functions perform the same actions.

The 6 functions also have some different, more complicated properties and relationships. You should check out this link if you want to read more.