Question

Question #3bb49

Answer 1

See below

Explanation:

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

Sine: `sintheta`
Cosine: `costheta`
Tangent: `tantheta=sintheta/costheta`

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

Cosecant: `csctheta = 1/sintheta`
Secant: `sectheta=1/costheta`
Cotangent: `cottheta=1/tantheta=1/(sintheta/costheta)=costheta/sintheta`

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.