How do you find the exact value of cos ( (2pi/3)-(pi/6))

kriauklasvt

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2022-08-20

How do you find the exact value of cos ( ( 2 π 3 ) ( π 6 ) )?

Answer & Explanation

Bobby Hodges

Bobby Hodges

Beginner2022-08-21Added 6 answers

Apply the trig identity: cos ( a b ) = cos a cos b + sin a sin b
cos ( 2 π 3 π 6 ) = cos ( 2 π 3 ) cos ( π 6 ) + sin ( 2 π 3 ) sin ( π 6 )
Trig table gives
cos ( 2 π 3 ) = 1 2 ; cos ( π 6 ) = 3 2
sin ( 2 π 3 ) = 3 2 ; sin ( π 6 ) = 1 2
Therefore:
cos ( 2 π 3 π 6 ) = ( 1 2 ) ( 3 2 ) + ( 3 2 ) ( 1 2 ) = 0

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