The Purplemath Forums

by **mannilea** on Wed Sep 09, 2009 2:35 pm

hi i was wondering if anyone could help me with this question

solve the equation 4 cot^2 x+12cosecx+1=0 giving all values of x to the nearest degree in the interval 0<x<360(should be equal to signs as well but comp doesnt do them)

thanks for any help much appreciated

**Sponsor**

by **stapel_eliz** on Wed Sep 09, 2009 6:33 pm

A good way to start is often to convert everything to sines and cosines, and see where that leads.

. . . . . $\frac{4\cos^2(x)}{\sin^2(x)}\, +\, \frac{12}{\sin(x)}\, +\, 1\, =\, 0$

In this case, that technique doesn't look very helpful. Try a Pythagorean identity instead:

. . . . . $4\left(1\, +\, \csc^2(x)\right)\, +\, 12\csc(x)\, +\, 1\, =\, 0$

. . . . . $4\csc^2(x)\, +\, 12\csc(x)\, +\, 5\, =\, 0$

This is a quadratic in cosecant. You can solve by factoring, and then solve the two resulting trigonometric equations. :wink:

by **mannilea** on Wed Sep 09, 2009 8:53 pm

hiya thanks for the answer not sure if you have worked it out or not but would the answer be 22.925 and 202.925 or not
thanks for any help

by **stapel_eliz** on Wed Sep 09, 2009 9:18 pm

What did you get when you plugged these values back into the original equation? If they worked, then they are solutions! :wink:

by **mannilea** on Wed Sep 09, 2009 10:28 pm

o right thank you didnt think of testing it lol

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solve the equation 4 cot^2 x + 12cosecx + 1 = 0 for 0<x<360

solve the equation 4 cot^2 x + 12cosecx + 1 = 0 for 0<x<360

Re: solve the equation 4 cot^2 x + 12cosecx + 1 = 0 for 0<x<360

Re: solve the equation 4 cot^2 x + 12cosecx + 1 = 0 for 0<x<360