Solving Interval Equation: cosec^2x=(3cotx+4)/2

[essaichay]

Hi everyone,

Trying to revise and I came across this question:


Solve the eqn cosec^2x = (3cotx + 4)/2, giving all values of x in the interval 0 < x < 2pi in radians to two dp.

I ended up with two principal values/angles (working in degrees at the moment), which are:

tan^-1(x) = 26.6 deg. and tan^-1(x) = -63.4 deg.

i used the formula pv + 180n, and got the right answers for -63.4 deg, which are:

2.03 rad and 5.18 rad, but when I applied the same forumla to solve tan^-1(x) = 26.6 deg

I got one wrong answer to the mark scheme: 6.74 rad (supposed to be 0.46 rad) but one right answer: 3.61 rad.

Completely confused on this as I'm sure I didn't misuse the formula.

Any suggestions on this would be great!
Thanks in advance.

 

[The|M|onster]

I think you are on the right track. The problem with 6.74 is that it doesn't fit in your interval. Keep in mind that you are dealing with radians and that 2 pi radians will take you all the way around the unit circle once. Try subtracting 2 pi from your answer (6.74) and look at what you get.