find the exact value of tan^(-1)(-1). write your answer in radians in terms of π. tan^(-1)(-1) =
find the exact value of tan^(-1)(-1). write your answer in radians in terms of π. tan^(-1)(-1) =
Answer
Explanation:
Step1: Recall inverse - tangent range
The range of (y = \tan^{-1}(x)) is ((-\frac{\pi}{2},\frac{\pi}{2})).
Step2: Find angle with tangent value
We know that (\tan\theta=\frac{\sin\theta}{\cos\theta}), and we want to find (\theta) such that (\tan\theta=- 1). In the unit - circle, (\tan\theta=-1) when (\sin\theta=-\cos\theta). In the range ((-\frac{\pi}{2},\frac{\pi}{2})), (\theta =-\frac{\pi}{4}) since (\tan(-\frac{\pi}{4})=\frac{\sin(-\frac{\pi}{4})}{\cos(-\frac{\pi}{4})}=\frac{-\frac{\sqrt{2}}{2}}{\frac{\sqrt{2}}{2}}=-1).
Answer:
(-\frac{\pi}{4})