posted by Kate on .
Hi I need some assistance on this problem
find the exact value do not use a calculator
Here is my attempt
RT = square root
pi = 3.14...
then I got this
(RT + 3RT)/3
1 - 3/3
as you can see this is a problem
because it leaves me with a denomenator of 0
well that will be in quadrant 4 since it is clockwise from the x axis due to the minus sign and 5 pi/12 is less than pi/2 or 6 pi/12.
call the x component of this vector a and the y component b. Then the magnitude of the cotan is a/b.
Notice that the angle to the negative y axis is 6pi/12 - 5pi/12 = pi/12
then the magnitude of tan pi/12 is a/b, just what we are looking for
so what is tan pi/12?
In degrees it is 15 degrees.
We know tan 30 degrees = 1/sqrt3 and sin 30 =1/2 and cos 30 = sqrt3 /2
so what is tan 15 degrees?
tan 15 = sin 30/(1+cos 30)
I think you can take it from there.
By the way remember it is in quadrant 4 so negative. I just used sizes in that 30, 60, 90 triangle and ignored signs.