Question

given than tan x = -2 and x is an angle in second quadrant, how do you find the other trignometric functions

Answer 1

Given tan x = -2
\[\rightarrow \tan x = \frac{-2}{1}=\frac{y}{x}\]

i.e. x= 1 and y=-2
now we are required to find r

Answer 2

since:
\[r^2=x^2+y^2 \rightarrow 1^2+(-2)^2=1+4=5 \rightarrow r= \sqrt5\]
Now
\[\sin x= \frac{y}{r}= \frac{-2}{\sqrt5}\]
\[\[\cos x= \frac{x}{r}= \frac{1}{\sqrt5}\]\]
similarly find other t-ratios