Inverse Cotangent Function

nee

Aug 2008
36
0
The question states:
Find the exact value of each real number y. Do not use a calculator.

y = arccot (
-√3)

What's the process for finding the answer???

 

dwsmith

MHF Hall of Honor
Mar 2010
3,093
582
Florida
The question states:
Find the exact value of each real number y. Do not use a calculator.

y = arccot (
-√3)

What's the process for finding the answer???

\(\displaystyle arccot=\frac{arccos}{arcsin}\rightarrow \frac{arccos(\frac{-\sqrt{3}}{2})}{arcsin(\frac{1}{2})}\)

\(\displaystyle arccos\bigg(\frac{-\sqrt{3}}{2}\bigg)=\frac{5\pi}{6}\)

or

\(\displaystyle arcsin\bigg(\frac{1}{2}\bigg)=\frac{5\pi}{6}\)
 
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Drexel28

MHF Hall of Honor
Nov 2009
4,563
1,566
Berkeley, California
\(\displaystyle arccot=\frac{arccos}{arcsin}\rightarrow \frac{arccos(\frac{-\sqrt{3}}{2})}{arcsin(\frac{1}{2})}\)

\(\displaystyle arccos\bigg(\frac{-\sqrt{3}}{2}\bigg)=\frac{5\pi}{6}\)

or

\(\displaystyle arcsin\bigg(\frac{1}{2}\bigg)=\frac{5\pi}{6}\)
\(\displaystyle \arctan(x){\color{red}\ne}\frac{\arcsin(x)}{\arccos(x)}\)