Question

given tan (0) = 4/3 and sin (0) =-4/5,find cos (0)

Answer 1

Tangent is defined as sin(x)/cos(x) in a unit circle, which is assumed. So, let's set it up:
$\frac{4}{3} = \frac{ -\frac{4}{5} }{cos(x)}$

Let's solve for cos(x):
$cos(x) = \frac{ -\frac{4}{5} }{ \frac{4}{3} }$

Simplify:
$cos(x) = -\frac{4}{5} * \frac{3}{4} = -\frac{12}{20} = -\frac{3}{5}$

And that's your answer!

Answer 2

The trig function tan is defined as follows:
tan(theta) = sin(theta) / cos(theta)

We are given that:
tan(theta) = 4/3
sin(theta) = -4/5

Substitute with the givens in the above equation to get cos(theta) as follows:
tan(theta) = sin(theta) / cos(theta)
4/3 = (-4/5) / cos(theta)
(4/3) cos(theta) = -4/5
20 cos(theta) = -12
cos(theta) = -12/20 = -3/5