Question

Find the exact value by using a half-angle identity.
cos(5π/12)

I know someone knows how to do this! if you could explain too, that'd be great!

Answer 1

os 5π/12
cos ((5 pi/6)/2) = +/- sqrt( (1+cos (5 pi/6))/2 )
cos(5 pi/6) = -sqrt(3)/2
cos (5 pi/12) = +/- sqrt( (2/2-sqrt(3)/2)/2 )
cos (5 pi/12) = +/- sqrt( ((2-sqrt(3))/2)/2 )
cos (5 pi/12) = sqrt( ( (2-sqrt(3))/4 ) )

5 pi/12 is in quadrant 1 so we choose the + sign because cos is positive there

Answer 2

thank you!!

Answer 3

your welcome

Answer 4

wait did you like re-expand the problem after cos(5 pi/6) = -sqrt(3)/2

Answer 5

most of these problems are some identities written on the unit circle.

Answer 6

okay.. well can you please explain each of the steps this person just gave me? i would reaaaalllyyyy appreciate it

Answer 7

ok so 5pi/12 is 75 degrees rite

Answer 8

i guess.. lol is it?

Answer 9

pi is 180 degrees.lol you know that rite and u muliply tht by 5 and get 900 and divide 12 and you get 75 degrees

Answer 10

okay but what does the 75 degrees have to do with the formula?

Answer 11

just to make ur question simpler... for example lets say it asked u for the cos of pi/6 which is 30 degrees.

Answer 12

there is some thing called the unit circle and it has this angles from 30,45,60,90 upto 360.. and since we have cos of Pi/6 which is 30 degrees. we can look at the unit circle for the cosine of 30 degrees and find it

Answer 13

@Dwade03 WHATS THE ANSWER?! D:

Answer 14

how is it done using half angle identity formula?!

Answer 15

ok so since they asked for cos(75) we can use the formula of using two angles to create that angle of 75. in this case we can use cos(45+35). u get tht?

Answer 16

@ganeshie8

Answer 17

so what in the world is the final answer? Is it cos(75)?