Question

i don't understand how to break this given theta , could u please help ?​

Answer 1

Answer:

hey here is your answer

pls mark it as brainliest pls

Step-by-step explanation:

$so \: here \\ sin( \frac{ - 11.\pi}{3} ) \\ = - sin( \frac{11.\pi}{3} ) \\ = - sin( \frac{11 \times 180}{3} ) \\ = - sin(11 \times 60) \\ \\ = - sin \: 660 \\ so \: here \: sin \: 660 \: can \: be \: represented \: as \: sin \: (720 - 60) \\ so \: 720 \: is \: nothing \: but \: 4\pi \\ so \: as \: we \: know \: that \\ whenever \: there \: is \: \pi \: there \: is \: no \: change \: in \: trigonometric \: ratio \\ hence \: then \\ - sin \: 660 = - sin \: 60 \\ so \: as \: sin \: 60 = \frac{ \sqrt{3} }{2} \\ \\ but \: as \: 660 \: lies \: in \: quadrant \: 4 \\ we \: know \: that \: except \: cos \: and \: sec \: all \: other \: trigonometric \: ratios \: are \: negative \\ hence \: - sin \: 660 = - ( - \frac{ \sqrt{3} }{2} ) \\ = \frac{ \sqrt{3} }{2} \\ hence \: - sin \: 660 \: ie \: sin \: ( - \frac{11\pi}{3} ) \: is \: \frac{ \sqrt{3} }{2}$