Applications Of Derivatives Question 151
Question: The angle between the curves $ y=\sin x $ and $ y=\cos x $ is
[EAMCET 2003]
Options:
A) $ {{\tan }^{-1}}(2\sqrt{2}) $
B) $ {{\tan }^{-1}}(3\sqrt{2}) $
C) $ {{\tan }^{-1}}(3\sqrt{3}) $
D) $ {{\tan }^{-1}}(5\sqrt{2}) $
Show Answer
Answer:
Correct Answer: A
Solution:
If $ \sin x=\cos x\Rightarrow x=\pi /4 $
If $ y=\sin x\Rightarrow {{( \frac{dy}{dx} )} _{x=\pi /4}}=\frac{1}{\sqrt{2}} $
If $ y=\cos x\Rightarrow {{( \frac{dy}{dx} )} _{x=\pi /4}}=\frac{-1}{\sqrt{2}} $
$ \tan \theta =\frac{m_1-m_2}{1+m_1m_2}=2\sqrt{2}\Rightarrow ,\theta ={{\tan }^{-1}}(2\sqrt{2}) $ .
BETA
