Question

As $\theta$ increases from $\frac{\pi }{4}$ to $\frac{5\pi }{4}$, the value of $4\cos \frac{1}{2}\theta$

• A. increases, then decreases
• B. decreases, and then increases
• C. decreases throughout
• D. increases throughout
• E. decreases, increases, and then decreases again

Answer 1

The correct option is C decreases throughout

$\cos x$ decreases in $(0,\pi )$

$\theta$ increases from $\frac{\pi }{4}$ to $\frac{5\pi }{4}$ then $\frac{\theta }{2}$ increases from $\frac{\pi }{8}$ to $\frac{5\pi }{8}$

$⟹4\cos \frac{\theta }{2}$ decreases throughout