Question

Given cos 0 = - 3/5 and cot A < 0, find the tan 0

Answer 1

Solution

Given that cos θ= 3/5 and cot x < 0, then tanθ = ?

Using trigonometric function and angle

$cos=\frac{adj}{hyp}$

USING PYTHAGORAS therorem

$\begin{gathered} adjacent=-3 \\ opposite=x \\ hypotenuse=5 \end{gathered}$

$\begin{gathered} hYP^2=OPP^2+ADJ^2 \\ 5^2=x^2+(-3)^2 \\ 25=x^2+9 \\ x^2=25-9 \\ x^2=16 \\ x=\sqrt{16} \\ x=4 \end{gathered}$

Tanθ = opposite/adjacent

$tan\theta=\frac{4}{-3}=-\frac{4}{3}$