Consider △dfe. what are the inputs or outputs of the following trigonometric ratios? express the ratios in simplest terms. = 4/5 cos(f) = ? tan(d) = ?

sin F = 4/5
cos F = 3/5
tan D = 3/4

Explanation:
First, we have sin an angle = 4/5
In a right-angled triangle:
sin theta = opposite / hypotenuse
This means that in triangle DFE:
The hypotenuse = 5 units
one of the sides = 4 units
Use Pythagoren theorem to get the other side as follows:
hypotenuse^2 = side1^2 + side2^2
5^2 = 4^2 + side2^2
side2^2 = 9
The second side of the triangle = 3 units

The special trig functions are as follows:
sin theta = opposite / hypotenuse
cos theta = adjacent / hypotenuse
tan theta = opposite / adjacent

From the attached figure and based on the calculations above:
sin F = 4/5
cos F = 3/5
tan D = 3/4

Hope this helps :)