2020 Nov P2 Q5

Question 5

The graphs of $f(x)=-\frac{\displaystyle 1}{\displaystyle 2}\cos x$ and $g(x)=\sin (x+30^{\circ})$ , for the interval $x\in[0^{\circ}\,;\,180^{\circ}]$ , are drawn below. $A(130,9^{\circ}\,;\,0,33)$ is the approximate point of intersection of the two graphs.

$5.1$	Write down the period of $g$ .	$(1)$
$5.2$	Write down the amplitude of $f$ .	$(1)$
$5.3$	Determine the value of $f(180^{\circ})-g(180^{\circ})$	$(1)$
$5.4$	Use the graphs to determine the values of $x$ , in the interval $x\in[0^{\circ}\,;\,180^{\circ}]$ , for which:
$\quad 5.4.1$	$f(x-10^{\circ})=g(x-10^{\circ})$	$(1)$
$\quad 5.4.2$	$\sqrt{3}\sin x+\cos x \geq 1$	$(4)$
		$\textbf{[8]}$