Question

What is the exact value of cos 5pi/4 radians?

Answer 1

I was thinking that i would draw a triangle but i didn't know which one?

Answer 2

5pi/4 radians = 225 degrees
it very familiar in trigono

Answer 3

what about the cos?

Answer 4

pi = 180

\[\cos\left(\frac{5\pi}{4}\right) = \cos\left(\frac{5(180)}{4}\right) = \cos(5(45)) = \cos(225) = -\frac{\sqrt{2}}{2}\]

Answer 5

cos225 is 1/sqrt(2)

Answer 6

@MCJones9879, cos(225) is in the 3rd quadrant so it has to be negative.

Answer 7

-1/sqrt(2) i meant .. sorry

Answer 8

Do i draw the triangle perpendicular to the y or x axis?

Answer 9

or -sqrt(2)/2

Answer 10

I'm not a big fan of drawing

Answer 11

Does it ask you to draw a triangle or just find the answer?

Answer 12

How'd you know it was - rad2/2?

Answer 13

@MCJones9879 No it doesn't but I'm just wondering how he got it

Answer 14

Unit circle bro

Answer 15

Depending on what quadrant you are in it will be positive or negative

Answer 16

that i now but what about the numbers?

Answer 17

Since you are asking for specfically cos it is negative since like Hero said, it is in the 3rd quadrant

Answer 18

you look up cos 225- on the unit circle being in the third quadrant

Answer 19

cos(225)=cos(45+180)

=cos45cos180+sin45sin180
=sqrt(2)/2*(-1)+sqrt(2)*(0)
=-sqrt(2)/2+0
=-sqrt(2)/2

Answer 20

Here is a link for quick answers for sin, cos, tan , cot, sec, and csc http://mathmistakes.info/facts/TrigFacts/learn/vals/sum.html

Answer 21

\[\sin(0, 30, 45, 60, 90) = \frac{\sqrt{0,1,2,3,4}}{2}\]
\[\cos(0, 30, 45, 60, 90) = \frac{\sqrt{4, 3, 2, 1, 0}}{2}\]

Answer 22

If you can understand it

Answer 23

Nobody wants to memorize a gigantic circle

Answer 24

@Hero I understand it

Answer 25

Well, that's great. The unit circle is okay to learn but there are much easier ways

Answer 26

Well, 5pi/4=225, so what you have me above wouldn't apply, right? Those numbers are way too low

Answer 27

or maybe I don't understand it?

Answer 28

You have to correspond them. 225 is a multiple of 45

Answer 29

every multiple of 45 is going to be \[±\frac{\sqrt{2}}{2}\]

Answer 30

Compare what I wrote with the unit circle. You'll start to see some correspondences.

Answer 31

All you need to do is memorize the first quadrant and you practically have the whole thing memorized. The only thing to pay attention to afterwards are the signs.

Answer 32

yea the quadrants, but thats simple, thnx a lot for helping me, helped a lot!