Find the Principal Value of cos-1(tan 3π/4)
Solution:
Given:
\[ y = \cos^{-1}\left(\tan \frac{3\pi}{4}\right) \]
Step 1: Evaluate tan(3π/4)
\[ \tan \frac{3\pi}{4} = -1 \]
So,
\[ y = \cos^{-1}(-1) \]
Step 2: Use principal value range
The principal value range of cos-1(x) is:
\[ [0, \pi] \]
We know:
\[ \cos(\pi) = -1 \]
Therefore,
\[ y = \pi \]
Final Answer:
Principal Value = \[ \pi \]