Finding the Value of an Inverse Trig Function

Date: 05/08/2000 at 20:01:16
From: Annette Granados
Subject: Inverse Trigonometric Functions

Find the value for

     cot[sin^-1(4/5)]

I don't understand how to use the formulas for this function.

Date: 05/09/2000 at 08:01:08
From: Doctor Jerry
Subject: Re: Inverse Trigonometric Functions

Hi Annette,

I'll use arcsin(x) for the inverse sine function. We want the 
cotangent of the arcsin(4/5), right?

Well, first, arcsin(4/5) lies between 0 and pi/2. We know this from 
the definition of the arcsine function.

     cot(y) = cos(y)/sin(y).

So,

     sin(arcsin(4/5)) = 4/5

and

     cos(arcsin(4/5))=3/5

So,

     cot(arcsin(4/5)) = (3/5)/(4/5) = 3/4.

You could also draw a small right triangle ABC, with a right angle at 
C. Think of A as the angle whose sine is 4/5. We can put a 5 on AC and 
a 4 on BC, because the sine of A is side opposite over hypotenuse. We 
see that AB is 3. So, cot(A) = 3/4.

- Doctor Jerry, The Math Forum
  http://mathforum.org/dr.math/