Question

The angle between the curves $y=\sin x$ and $y=\cos x$ is

• A. $\tan ^{-1}(2 \sqrt{2})$
• B. $\tan ^{-1}(3 \sqrt{2})$
• C. $\tan ^{-1}(3 \sqrt{3})$
• D. $\tan ^{-1}(5 \sqrt{2})$

Answer 1

Answer: (A)

If $\sin x=\cos x \Rightarrow x=\frac{\pi}{4}$
$y=\sin x \Rightarrow\left(\frac{d y}{d x}\right)_{x = \pi / 4}=\frac{1}{\sqrt{2}}$
If $y=\cos x \Rightarrow\left(\frac{d y}{d x}\right)_{x = \pi / 4}=-\frac{1}{\sqrt{2}}$
$\tan \theta=\frac{m_1-m_2}{1+m_1 m_2}=2 \sqrt{2} \Rightarrow \theta=\tan ^{-1}(2 \sqrt{2})$