Question : What is the value of $\operatorname{cos}\left(-\frac{17 \pi}{3}\right)$?
Option 1: $1$
Option 2: $\frac{\sqrt{3}}{2}$
Option 3: $\frac{1}{2}$
Option 4: $0$
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Correct Answer: $\frac{1}{2}$
Solution :
$\operatorname{cos}\left(-\frac{17 \pi}{3}\right)$
$=\operatorname{cos}\left(\frac{17 \pi}{3}\right)$
$=\operatorname{cos}\left(\frac{17\times 180º}{3}\right)$
$=\operatorname{cos}\left(17\times 60º\right)$
$=\operatorname{cos}\left(1020º\right)$
$=\operatorname{cos}\left(90º\times 11+30º\right)$
$=\operatorname{sin}\left(30º\right)$
$=\frac{1}{2}$
Hence, the correct answer is $\frac{1}{2}$.
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