My Math Forum 2 quick inverse Trig questions

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 November 9th, 2008, 04:59 PM #1 Newbie   Joined: Sep 2008 Posts: 7 Thanks: 0 2 quick inverse Trig questions I just got a math worksheet today on inverse trig functions... i just have a quick question on how to word my answer. The 2 Problems sin^-1[sin (3pi/4)] cos^-1[cos(-pi/3)] I know that the inverse sin and inverse cos functions have domains... Doesn't the quantities of the brackets fall outside of the domain of the graphs??? I am wondering how I would write the answer to my teacher? Would I put N/A, Falls outside range, ETC. I don't know what to put... Also one of my problems says to simplify tan(cos^-1 2x) How in the world would I do that? THANKS FOR ALL HELP
November 11th, 2008, 08:53 AM   #2
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Quote:
 Originally Posted by packerfan128 The 2 Problems sin^-1[sin (3pi/4)] cos^-1[cos(-pi/3)] I know that the inverse sin and inverse cos functions have domains... Doesn't the quantities of the brackets fall outside of the domain of the graphs?
No. These are easily evaluated mentally. To check your answers, use a calculator.

Quote:
 Originally Posted by packerfan128 Also one of my problems says to simplify tan(cos^-1 2x) How in the world would I do that?
Find cos(cos^-1 2x). What is the reciprocal of that? Now use the identity $\tan^2A\,=\,\sec^2A\,-\,1.$

November 11th, 2008, 09:19 AM   #3
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Re: 2 quick inverse Trig questions

#1. The quantities inside are just numbers. The inverse function might restrict the number of results of the angle whose cosine is that number, for example.

HINT #2: [attachment=0:1yv5fiwd]Image1.jpg[/attachment:1yv5fiwd]
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