Hi, folks I'm curious about a question I've been doing for an upcoming math assignment. I have a professor who is really bad in English and unfortunately has made me really confused with this question and I need to know if I've got the methodology right, and if I haven't, why not. I'm going to show my current train of thought on this question and corrections would be appreciated. :)
If cos(t) = -3/4 with pi < t < 3pi/2, find the following
cos(-t) = cos(t)
sin(-t) = -sin(t)
tan(-t) = -tan(t)
sec(-t) = sec(t)
csc(-t) = -csc(t)
cot(-t) = -cot(t)
The Attempt at a Solution
a) cos(-t) = cos(t) so cos(-t) = -3/4 = -√3/2
b) sec(-t) = sec(t)
So we know that sec(t) = 1/x, and we also know that cos = x. Therefore -3/4 is equal to x.
So 1/(-3/4) = -4/3 =-2/√3 = -(2√3)/3 <-- That is beyond -1 and therefore I don't think it is possible...
c) sin(-t) = -sin(t) and we know that sin(t) = y, and we know that (cos, sin) that sin is equal to y. We also know that cos = -√3/2 and that this is one of the identities of 30 degrees and that the corresponding y or sin for 30 degrees is 1/2. Therefore sin = -1/2
Thank you for your time. ^^