Question

The exact value of cos(pi/4) is 1/square root 2
but when working out cos (-7pi/4) why is the answer square root 2/2 ?

Answer 1

cos is an even function \[\huge\rm Cos(-x)=\cos(x)\]
what is cos at 7pi/4 radi ??

Answer 2

I have no idea, can you explain it to me further. I got pi/4

Answer 3

so how did you get pi/4 ?? :=)

Answer 4

r u allowed to use unit circle ?:=)

Answer 5

by going around the unit circle a lot ?? yes i am

Answer 6

alright

Answer 7

(x,y) solution where c-coordinate represent cos
and y-coordinate = sin
so what is cos at 7pi/4 ?

Answer 8

and no pi/4 isn't \[\huge\rm \frac{ 1 }{ \sqrt{2} }\]you can't leave the root at the denominator
you have to multiply both top and bottom of the fraction by square root 2

Answer 9

how do i find the value of these coordinates if i am not given the unit circle ??

Answer 10

oh! so i just have to make sure there are no square roots at the denominator ??

Answer 11

and i will get the coordinates i am looking for? thanks!!

Answer 12

yes right \[\textrm {no square root at the denominator }\]

Answer 13

without looking at the unit circle
2 ways
1) familiar with the 30-60-90 and 45-45-90 triangle
2nd) memorize

Answer 14

and for example if they ask `what is the exact value of cos(5pi/4)
then cos equal to -sqrt{2} over 2