Question

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

Answer 1

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

Answer 2

Tangent is defined as sin(x)/cos(x) in a unit circle, which is assumed. So, let's set it up:

`(4)/(3) = ( -(4)/(5) )/(cos(x))`

Let's solve for cos(x):

`cos(x) = ( -(4)/(5) )/( (4)/(3) )`

Simplify:

`cos(x) = -(4)/(5) * (3)/(4) = -(12)/(20) = -(3)/(5)`

And that's your answer!