Finding the Value of an Inverse Trig FunctionDate: 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/ |
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