How do you find tan and cot if cot = 12/5 and sin <0?

1 Answer
Manikandan S.
May 2, 2015

Easy steps I assume you have to calculate tan and cos

#tan theta = 1/cot theta#
#tan theta = 5/12#
#sin theta/cos theta = 5/12#
#12sin theta-5cos theta = 0#
#sin^2 theta + cos^2 theta =1#
Assume #sin theta =x ; cos theta = y#
#x^2+y^2 = 1#
#12x-5y=0#
#y=(12x)/5#
#x^2+(144x^2)/25=1#
#x^2(1+(144)/25) = 1#
#x^2 = 1/(169/25)#
#x^2 = (5/13)^2#
#x = +-5/13#
# sin theta = +-5/13#
As #sin theta <0 ,# #sin theta = -5/13#
#cos theta = -12/13#

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