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trig

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I am very confused about the concepts of..
sin è = sin(180 - è)
sin (180 + è)= -sinè
tan (180 - è) = -tanè

and how the final answer was found in this problem...

Find cos 510:

cos510=cos(540-30)
=-cos30
=-s.r3/2

i don't understand how we went from -cos 30 to -s.r3/2 ?

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