Question #3bb49

1 Answer
Jan 27, 2018

Answer:

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.