question 3 evaluate the following expressions. your answer must be an exact angle in radians and in the…

question 3 evaluate the following expressions. your answer must be an exact angle in radians and in the interval (-π/2, π/2). example: enter pi/6 for π/6. (a) tan^(-1)(1)= (b) tan^(-1)(-√3/3)= (c) tan^(-1)(-1)= question help: video 1 video 2 submit question

question 3 evaluate the following expressions. your answer must be an exact angle in radians and in the interval (-π/2, π/2). example: enter pi/6 for π/6. (a) tan^(-1)(1)= (b) tan^(-1)(-√3/3)= (c) tan^(-1)(-1)= question help: video 1 video 2 submit question

Answer

Explanation:

Step1: Recall inverse - tangent values

The inverse - tangent function, $y = \tan^{-1}(x)$, gives the angle $\theta$ such that $\tan(\theta)=x$ and $\theta\in(-\frac{\pi}{2},\frac{\pi}{2})$.

Step2: Solve for (a)

We know that $\tan(\frac{\pi}{4}) = 1$. So, $\tan^{-1}(1)=\frac{\pi}{4}$.

Step3: Solve for (b)

We know that $\tan(-\frac{\pi}{6})=-\frac{\sqrt{3}}{3}$. So, $\tan^{-1}(-\frac{\sqrt{3}}{3})=-\frac{\pi}{6}$.

Step4: Solve for (c)

We know that $\tan(-\frac{\pi}{4})=-1$. So, $\tan^{-1}(-1)=-\frac{\pi}{4}$.

Answer:

(a) $\frac{\pi}{4}$ (b) $-\frac{\pi}{6}$ (c) $-\frac{\pi}{4}$