Question

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

Answer 1

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`