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

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

Guest Mar 7, 2015

#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
#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
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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.

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

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

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?

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

Melody  Mar 8, 2015
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Here's WolframAlpha's result:

.

Alan  Mar 8, 2015
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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
+92751
+5