4. which of the following functions will result with a value of 1/2? (0.5 point) a sin(9π/2) b cos(19π/6) c…

Explanation:

Step1: Simplify sin(9π/2)

$\sin\left(\frac{9\pi}{2}\right)=\sin\left(4\pi+\frac{\pi}{2}\right)=\sin\left(\frac{\pi}{2}\right) = 1$

Step2: Simplify cos(19π/6)

$\cos\left(\frac{19\pi}{6}\right)=\cos\left(2\pi + \frac{7\pi}{6}\right)=\cos\left(\frac{7\pi}{6}\right)=-\frac{\sqrt{3}}{2}$

Step3: Simplify sin(-17π/6)

$\sin\left(-\frac{17\pi}{6}\right)=-\sin\left(\frac{17\pi}{6}\right)=-\sin\left(2\pi+\frac{5\pi}{6}\right)=-\sin\left(\frac{5\pi}{6}\right)=-\frac{1}{2}$

Step4: Simplify cos(11π/3)

$\cos\left(\frac{11\pi}{3}\right)=\cos\left(4\pi-\frac{\pi}{3}\right)=\cos\left(-\frac{\pi}{3}\right)=\cos\left(\frac{\pi}{3}\right)=\frac{1}{2}$

Answer:

D. $\cos\left(\frac{11\pi}{3}\right)$

Explanation for question 5:

Step1: Find sin(π/6)

$\sin\left(\frac{\pi}{6}\right)=\frac{1}{2}$

Step2: Find sin(-11π/6)

$\sin\left(-\frac{11\pi}{6}\right)=-\sin\left(\frac{11\pi}{6}\right)=-\sin\left(2\pi - \frac{\pi}{6}\right)=\sin\left(\frac{\pi}{6}\right)=\frac{1}{2}$

Step3: Find cos(270°)

$\cos(270^{\circ}) = 0$

Step4: Find cos(-90°)

$\cos(-90^{\circ})=\cos(90^{\circ}) = 0$

Step5: Find tan(-3π/4)

$\tan\left(-\frac{3\pi}{4}\right)=-\tan\left(\frac{3\pi}{4}\right)=-\tan\left(\pi-\frac{\pi}{4}\right)=\tan\left(\frac{\pi}{4}\right)=1$

Step6: Find tan(5π/4)

$\tan\left(\frac{5\pi}{4}\right)=\tan\left(\pi+\frac{\pi}{4}\right)=\tan\left(\frac{\pi}{4}\right)=1$

Answer:

Trigonometric Functions	Value
$\sin\left(\frac{\pi}{6}\right)$	$\frac{1}{2}$
$\sin\left(-\frac{11\pi}{6}\right)$	$\frac{1}{2}$
$\cos(270^{\circ})$	$0$
$\cos(-90^{\circ})$	$0$
$\tan\left(-\frac{3\pi}{4}\right)$	$1$
$\tan\left(\frac{5\pi}{4}\right)$	$1$