Question

if tan θ = 12/5 and cos θ<0, what is sin θ?

Answer 1

these are the choices https://gyazo.com/28d732e17e4f4c5ffd4ee0233aa34194

Answer 2

hint:
using data of the exercise, we have the subsequent drawing:

namely the subsequent condition holds:
\(\pi < \theta <3 \pi/2\)

Answer 3

now we have to apply this condition:
\[{\left( {\cos \theta } \right)^2} + {\left( {\sin \theta } \right)^2} = 1\]
where:
\[\sin \theta = \frac{5}{{12}}\cos \theta \]
please replace \(\sin \theta\) from second formula into the first one, and solve for \(\cos \theta\)

Answer 4

oops.. the second formula, is:
\[\sin \theta = \frac{{12}}{5}\cos \theta \]

Answer 5

and here is the right drawing: