Question

How do I find trig inverses?
The current question is arctan(sqrt(3)), but I'd like to know how to do this for all arc- questions

Answer 1

@Hero

Answer 2

atan(sqrt(3))=?
acos
asin

Answer 3

...I'm not following o.O

Answer 4

arctan (sqrt(3)) is asking for arctangent of 1.732
Let's stick with regualr numbers for a start
arctangent (1.2) is asking "What angle has a tangent of 1.2"?
Understand so far?

Answer 5

I understand what arctangent, arcsine, and arccosine ask for. I also figured out the answer. I'm curious if there is a method to solve without knowing the unit circle.

Answer 6

Well a calculator will give you the answer.
Back in the old days when we looked up trig functions in tables, we would look up the value in the reverse order. By that I mean we would look at the values and then match it up to the proper angle.

Answer 7

The arctangent question was simplistic, because pi/3 was simple enough to see as the answer once I looked at a unit circle. The problem is when I come across questions with numbers that aren't available on the unit circle.

For example, the next equation is cos(2arcsin(5/13)). 5/13 not being relevant to the unit circle, I'm at a loss of what to do next

Answer 8

That's what I did to find the answer for arctan of sqrt of 3

Answer 9

Then you'd have the same problem with looking up tangents too.
For example what is the tangent of .2?

Answer 10

No idea

Answer 11

So basically you want to know how to calculate tangents and arctangents? I believe it is a pretty complicated process.

Answer 12

So there's no simplistic way without a calculator?

Answer 13

A calculator or tables.
Here's a good online calculator:
http://www.1728.org/trigcalc.htm

Answer 14

Thank you, sir

Answer 15

Okay.
By the way some of those calculations can be very complcated.
Ever see the formula for computing PI?
It is NOT very simple

Answer 16

Well math is all about loopholes so you never know :)

Answer 17

Math does have some loopholes but sometimes the answer lies in serious calculations.