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Inverse trig functions

Date: Wed, 14 Dec 1994 15:17:46 -0500 (EST)
From: Lizzy Hechenbleikner
Subject: Calculus Help

I am trying to evaluate this:

cot[sin^-1 (-1) + 2sec^-1 (-2)]

In other words... cotangent of inverse sine of negative one plus two 
times inverse secant of negative 2.

Please help, thanks

Date: Wed, 14 Dec 1994 17:21:39 -0500 (EST)
From: Dr. Ken
Subject: Re: Calculus Help

Hello there!

Basically, this problem revolves on your ability to deal with the 
inverse trigonometric functions.  For instance, to evaluate Sin^-1 (-1), 
you ask yourself "what angle has a Sine of -1?"  If you look at the 
graph of the Sine function, or at the unit circle, you see that the 
angle -90 degrees has the right Sine.  So this is that part of the 

Then to find Sec^-1 (-2), you remember that Secant is the reciprocal 
of Cosine.  So you ask yourself "what angle has a cosine of 1/2?"  
Then you look at the unit circle, and you say "Aha!  It's 60 degrees!  
Pi/3 radians!"  So this is that part of the answer.

Then you have Cot[-90 + 2*60] = Cot[30] = 1/Tan[30] = Sqrt{3}.

I hope this helps you out, and write back if you need more help!

-Ken "Dr." Math
Associated Topics:
High School Trigonometry

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