Question

$\cot( theta ) = 3 \div 4 \: and \: theta - a = 90 \: find \: a \:$

Answer 1

Given cot (x) = 3/4, ( let theta be x)
so,
cos (x) / sin (x) = 3/4

cos (x) = sin (90 - x)
sin (x) = cos (90 - x)

so,
sin (90 - x) / cos (90 - x) = 3/4

but Given that, x - a = 90
so,
-a = 90 - x

on substituting in the main equation,
we get,
sin (-a) / cos (-a) = 3/4

but,
sin (-a) = -sin(a) and cos (-a) = cos (a)

so,
-tan (a) = 3/4

a = tan^-1 (-3/4)

a = -36.86°

Hope this helps

- WonderGirl