GATE Chemical 2018 | GA | Question: 3

Question

For $0\leq{x}\leq{2\pi}$, $\sin x \text{ and } \cos x$ are both decreasing functions in the interval _________ .

• A. $\left(0,\dfrac{\pi}{2}\right)$
• B. $\left(\dfrac{\pi}{2},\pi\right)$
• C. $\left(\pi,\dfrac{3\pi}{2}\right)$
• D. $\left(\dfrac{3\pi}{2},2\pi\right)$

Answer 1

Both functions are decreasing in the interval $(\pi/2, \pi )$

Comments

And it is increasing in the interval $\left ( \frac{3\pi }{2},2\pi \right )$, right?

Answer 2

Answer will be C)

As, Sin is -ve in the interval 3rd and 4th quadrant of axis and Cos -ve for 2nd and 3rd quadrant of axis

Comments

here not ask nigative value edit your answer

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That’s right, but if we solve it using definition, which is f’(x)<0 then both function will be -Ve in the interval $(\prod, 3\prod/2)$

Answer 3

From π/2 to π, both sin x and cos x are Decreasing functions.
So Option B is correct.