answer: \n# 8 $y = csc x cot x, y(\frac{pi}{2}) = 6$\nto advance in the circuit, locate $y(\frac{11pi}{6})$.
answer: \n# 8 $y = csc x cot x, y(\frac{pi}{2}) = 6$\nto advance in the circuit, locate $y(\frac{11pi}{6})$.
Answer
Explanation:
Step1: Integrate (y')
We know that (\int\csc x\cot xdx =-\csc x + C). So (y =-\csc x + C).
Step2: Find (C)
Given (y(\frac{\pi}{2}) = 6). Substitute (x=\frac{\pi}{2}) into (y =-\csc x + C). Since (\csc\frac{\pi}{2}=1), we have (6=-1 + C), then (C = 7). So (y=-\csc x+7).
Step3: Calculate (y(\frac{11\pi}{6}))
Substitute (x = \frac{11\pi}{6}) into (y=-\csc x+7). Since (\csc\frac{11\pi}{6}=\csc(2\pi-\frac{\pi}{6})=-\csc\frac{\pi}{6}=-2), then (y= -(-2)+7=9).
Answer:
(9)