Question

Find the exact value of tan^-1(-1) . Write your answer in radians in terms of ∏ .

Answer 1

\(\bf tan^{-1}(-1)=\theta\quad means\quad tan(\theta)=-1\quad \textit{now recall that}\\ \quad \\
tan(\theta)=\cfrac{sin(\theta)}{cos(\theta)}\implies \cfrac{y}{x}\)

the only way a fraction will turn up to be 1, is when you have the same above and below, that is \(\bf \cfrac{same}{same}=1\)

you can only get -1 from that, if EITHER above or below is negative, that is \(\bf \cfrac{-same}{same}=-1\qquad \cfrac{same}{-same}=-1\)

now check your Unit Circle for where the cosine or "x" and the sine or "y" are the same value, but different signs, that's where the tangent will be -1, and thus the angles