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acot(sec(acsc -2sqrt 3/2))

Guest Mar 7, 2015

Best Answer 

 #12
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This question illustrates the need for people to put brackets in their questions so that the intended question is actually answered!

Melody  Mar 9, 2015
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 #1
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It appears that you may be missing a parentheses around (-2sqrt 3/2).

If that is the case, then using trig identities the answer should be 47.45 degrees.

Start by considering that the arccsc is 1/sin, sec is 1/cos, and cot is 1/tan.

Guest Mar 7, 2015
 #2
avatar+91469 
+5

Thanks anon.

I am having problems getting my head around this so I'd like another mathematician to take a look please.

 

acot(sec(acsc -2sqrt 3/2))

I also will interpret this as   acot(sec(acsc( -2sqrt 3/2)))   but you really did need brackets here.

 

$$acot(sec(acsc( \frac{-2\sqrt 3}{2})))\\\\
=acot(sec(acsc( -\sqrt 3))\\\\
=acot(sec(asin( \frac{1}{-\sqrt 3}))\\\\
NOTE \;\;asin( \frac{1}{-\sqrt 3})\quad $is an angle in the 4th quadrant$\\\\
$And sec of an angle in the 4th quad is positive$\\\\
=acot(\frac{\sqrt3}{\sqrt2})\\\\
=atan(\frac{\sqrt2}{\sqrt3})\\\\
=atan\sqrt{\frac{2}{3}}\\\\$$

 

$$\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{tan}}^{\!\!\mathtt{-1}}{\left({\sqrt{{\frac{{\mathtt{2}}}{{\mathtt{3}}}}}}\right)} = {\mathtt{39.231\: \!520\: \!483\: \!592^{\circ}}}$$

 

That is what I get but I'd really like someone else to look at it please.

Even if it is correct, is there an easier way of working it through?

ADDED

I ran this question through Wolfram|Alpha and got the same answer

 

Melody  Mar 8, 2015
 #10
avatar+26403 
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Here's WolframAlpha's result:

trig.

.

Alan  Mar 8, 2015
 #11
avatar+91469 
+5

Hi Alan,

You have not answered the same question as I did, and neither of us answered the question that was actually asked.  I think that this is quite funny.

 

I'm going to try and answer the original question.

 

acot(sec(acsc -2sqrt 3/2))

I think technically this should be interpreted as;

 

$$\\acot(sec(\frac{acsc (-2) *\sqrt 3)}{2}))\\\\
=acot(sec(\frac{asin (\frac{1}{-2}) *\sqrt 3)}{2}))\\\\
=acot(sec(\frac{\frac{-\pi}{6} *\sqrt 3)}{2}))\\\\
=acot(sec(\frac{-\sqrt 3\pi}{12} ))\\\\$$

 

$${sec}{\left({\mathtt{\,-\,}}{\frac{\left({\frac{{\mathtt{180}}}{{\mathtt{\pi}}}}\right){\mathtt{\,\times\,}}{\sqrt{{\mathtt{3}}}}{\mathtt{\,\times\,}}{\mathtt{\pi}}}{{\mathtt{12}}}}\right)} = {\mathtt{1.112\: \!419\: \!829\: \!676\: \!128\: \!1}}$$

 

$${acot}{\left({sec}{\left({\mathtt{\,-\,}}{\frac{\left({\frac{{\mathtt{180}}}{{\mathtt{\pi}}}}\right){\mathtt{\,\times\,}}{\sqrt{{\mathtt{3}}}}{\mathtt{\,\times\,}}{\mathtt{\pi}}}{{\mathtt{12}}}}\right)}\right)} = {\mathtt{41.953\: \!677\: \!923\: \!85^{\circ}}}$$

 

Check with Wolfram|Alpha

 

Melody  Mar 9, 2015
 #12
avatar+91469 
+5
Best Answer

This question illustrates the need for people to put brackets in their questions so that the intended question is actually answered!

Melody  Mar 9, 2015

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