SOLUTION: Use a cofunction to write an expression equal to cos {{{(2pi/7)}}}

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Question 855196: Use a cofunction to write an expression equal to cos %282pi%2F7%29
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
cofunctions are:
sin(x) = cos(90-x)
tan(x) = cot(90-x)

you want to find the cofunction of cos(2pi/7)
that would be sin(90 degrees - 2pi/7)
90 degrees is equal to pi/2, so you would get:
cos(2pi/7) = sin(pi/2 - 2pi/7).
pi/2 is equivalent to 7pi/14
2pi/7 is equivalent to 4pi/14
your equation becomes:
cos(2pi/7) = sin(7pi/14 - 4pi/14) which can be simplified to:
cos(2pi/7) = sin(3pi/14)
use your calculator to find cos(2pi/7) and sin(3pi/14).
they should be equal to each other.
make sure your calculator is in radians mode, or get the equation in equivalent degree mode and use your calculator in degree mode.
i switched my calculator to radian mode and got:
.6234898019 = .6234898019
since they are equal, the cofunctions are correct.
to switch from radians to degrees, multiply by 180 and divide by pi.
when you do that:
2pi/7 becomes 2pi/7 * 180/pi = 51.42857143 degrees.
3pi/14 becomes 3pi/14 * 180/pi = 38.57142857 degrees.
switch your calculator back to degree mode and you get:
cos(51.42857143) = .6234898018
sin(38.57142857) = .6234898018
here's a reference on cofunctions:
http://www.regentsprep.org/Regents/math/algtrig/ATT6/cofunctions.htm