Question

Find Sin x and Tan x if Cos x= 2/3 and Cot x >0. Evaluate without using calculator.

Answer 1

to solve this proble we need to know the definition for the trigonometric functions using the right triangule

using this triangule we can fing the trig.

$\sin =\frac{opp}{hyp};\cos =\frac{adj}{hyp};\tan =\frac{opp}{adj}$

since we now that the cot is +, all sides must be in the same sign, meaning that we can draw the tiangle on quad 1 or 3

using this we can draw the triangle.

use the pytaghorean to find the missing side

$\begin{gathered} h^2=ad^2+op^2 \\ op=\sqrt[]{h^2-ad^2} \\ op=\sqrt[]{3^2-2^2} \\ op=\sqrt[]{5} \end{gathered}$

rewrite the trigonometric functions

$\sin =\frac{\sqrt[]{5}}{3};\tan =\frac{\sqrt[]{5}}{2}$