Answer:
\(\tan x=\frac{4}{3}\)
Step-by-step explanation:
Given : \(\sin x=\frac{4}{5}\) and \(\cos x=\frac{3}{5}\)
We have to find the ratio for \(\tan x\)
Consider the trigonometric ratio, we know the ratio of sine and cosine is tangent.
Written mathematically as,
\(\tan x=\frac{\sin x}{\cos x}\)
Substitute, we get,
\(\tan x=\dfrac{\frac{4}{5}}{\frac{3}{5}}\)
Simplify, we have,
\(\tan x=\frac{4\times 5}{5 \times 3}\)
Simplify , we get,
\(\tan x=\frac{4}{3}\)
Thus, \(\tan x=\frac{4}{3}\)
