# Math Help - Solve trig equation

1. ## Solve trig equation

Solve 3cot^2x+8cosec^2x+1=0, giving all the values in degrees the range 0<x<360

Ok, so I have replaced 3cot^2x with 3cosec^2x-3, to give 3cosec^2x+8cosec^2x-2=0
From here, I have used the quadratic formula giving me cosecx = 0.230.. and cosecx= -2.896...
and then I don't know how to proceed

2. ## Re: Solve trig equation

Unit circles. Draw a unit circle and see where all those cosecants might lie.

BTW, there's no way that a cosecant can equal 0.230. Think about why. (Hint: you made a mistake somewhere.)

3. ## Re: Solve trig equation

Originally Posted by Bernana
Solve 3cot^2x+8cosec^2x+1=0, giving all the values in degrees the range 0<x<360

Ok, so I have replaced 3cot^2x with 3cosec^2x-3, to give 3cosec^2x+8cosec^2x-2=0
From here, I have used the quadratic formula giving me cosecx = 0.230.. and cosecx= -2.896...
and then I don't know how to proceed

5. ## Re: Solve trig equation

Sorry, I didn't copy the equation down correctly. It is 3cot^2x+8cosecx+1=0

6. ## Re: Solve trig equation

Originally Posted by Bernana
Sorry, I didn't copy the equation down correctly. It is 3cot^2x+8cosecx+1=0

7. ## Re: Solve trig equation

The solutions are 200° and 340°
I found sinx=-0.345 ... or sinx=4.345...
but I cannot get to the solutions from here

8. ## Re: Solve trig equation

Originally Posted by Bernana
The solutions are 200° and 340°
I found sinx=-0.345 ... or sinx=4.345...
but I cannot get to the solutions from here
Do you really accept sinx = 4.345? This solution is to be rejected. Why?

using your calculator and to obtain arcsin(-0.345). the calculator is not going to give you exactly 200 unless your calculator does better job than mine, it is going to be 200.19. The 200 and 300 are rounded numbers.

9. ## Re: Solve trig equation

Just to put my two cents in, I typically keep 7 or 8 decimal points until I get to the end of the calculation.

-Dan

10. ## Re: Solve trig equation

Originally Posted by topsquark
Just to put my two cents in, I typically keep 7 or 8 decimal points until I get to the end of the calculation.

-Dan
This is what I usually do when conversion to minutes and seconds angles. In this problem, three decimal places did not give me any better than 10 decimal places since the answer is going to be rounded to integers 200 and 300