Question

In which of the following interval(s) of $x,$
$\cos x>0\forall x\in (\pi ,6\pi )$

• A. $(\frac{7\pi }{2},\frac{9\pi }{2})$
• B. $(\frac{11\pi }{2},6\pi )$
• C. $(\frac{3\pi }{2},\frac{5\pi }{2})\cup (\frac{7\pi }{2},\frac{9\pi }{2})\cup (\frac{11\pi }{2},6\pi )$
• D. $(\frac{3\pi }{2},\frac{5\pi }{2})$

Answer 1

Answer: (A), (B), (C), (D)

$(\frac{3\pi }{2},\frac{5\pi }{2})$

Given: $y=\cos x\forall x\in (\pi ,6\pi )$

Now, we want to find the region in $(\pi ,6\pi )$ for which $\cos x>0$
Using the graph of $\cos x:$


$\Rightarrow \text{For}x\in (\pi ,6\pi ),\cos x>0$
$\Rightarrow x\in (\frac{3\pi }{2},\frac{5\pi }{2})\cup (\frac{7\pi }{2},\frac{9\pi }{2})\cup (\frac{11\pi }{2},6\pi )$