find the exact value of the real number y.\n\n( y=\tan ^{-1}(1) )\n\na. ( -\frac{pi}{4} )\nb. ( \frac{3…
find the exact value of the real number y.\n\n( y=\tan ^{-1}(1) )\n\na. ( -\frac{pi}{4} )\nb. ( \frac{3 pi}{4} )\nc. ( \frac{pi}{4} )\nd. 0
Answer
Explanation:
Step1: Recall the range of (y = \tan^{-1}(x))
The range of (y=\tan^{-1}(x)) is (\left(-\frac{\pi}{2},\frac{\pi}{2}\right))
Step2: Find the value of (x) for which (\tan(x)=1)
We know that (\tan\left(\frac{\pi}{4}\right) = 1) and (\frac{\pi}{4}\in\left(-\frac{\pi}{2},\frac{\pi}{2}\right))
Answer:
C. (\frac{\pi}{4})