Question

how come pi/4 equals sqrt2/2?

Answer 1

rationalize the denominator

Answer 2

unit circle

Answer 3

actually only sinx and cosx has sqrt(2) / 2 tan 45 is 1

Answer 4

Maybe you mean cos(pi/4) or sin(pi/4) instead of pi/4 ?

Answer 5

yes cos pi/4

Answer 6

why does it equal sqrt2/2?

Answer 7

look at the unit circle, pi/4 = sqrt (2) / 2
for the cos value
the coordinates for the polar coordinate system is (cos,sin).

Answer 8

draw the right triangle of 45 degrees.

Answer 9

http://image.tutorvista.com/cms/images/38/unit-circle.JPG
You can see here, that at 45 degrees or pi /4 .
The value for cosine is sqrt 2 / 2

Answer 10

if only draw WOULD WORK ON HERE THAT WOULD BE GREATTTTTTTTTTTTTT

Answer 11

What is the length of the hypotenuse?

Answer 12

missing sqrt(2)

Answer 13

And you can then find the value of cos(pi/4)

Answer 14

@UsukiDoll I was asking him to find the missing side.

Answer 15

uh oh! sorry X<X

Answer 16

the problem says use the fact that trig functions are periodic to find the exact value of cos 17pi/4

Answer 17

ok first multiply by 180 / pi

Answer 18

I can't draw, damn it! I need drawing to freaking do trig.

Answer 19

same here ! ! !

Answer 20

I can't draw the triangles

Answer 21

IT'S TWIDDLA TIME! :D

Answer 22

http://www.twiddla.com/1470501

Answer 23

there now we can draw!

Answer 24

Subtract multiples of 2pi from 17pi/4... since 2pi is a full revolution

17pi/4 - 16pi/4 =

Answer 25

16pi/4 = 4pi, a multiple of 2pi

Answer 26

hypotenuse = 1
first leg = x
second leg = y


We know x^2 + y^2 = 1^2
We also know that x = y
x^2 + x^2 = 1^2
2 * x^2 = 1
x^2 = 1/2
x = 1/sqrt(2)

Answer 27

I know that I have to find the biggest multiple of 2 smaller than 17/4 then find the number to complete
which would be pi/4 I just don't know why it equals sqrt2/2

Answer 28

When you rationalize the denominator:
1/sqrt(2) * sqrt(2) / sqrt(2) = sqrt(2) / 2

Answer 29

is my suggestion being completely ignored? -_-
after you do what agent does, you look at the unit circle...
polar coordinates are in (cos,sin) form.
pi/4 on the unit circle is (sqrt(2)/sqrt(2)/2)
http://image.tutorvista.com/cms/images/38/unit-circle.JPG

Answer 30

It's much simpler than that D:

Answer 31

(sqrt(2)/2,sqrt(2)/2) *

Answer 32

Looking at the unit circle is much simpler than doing what you are doing..

Answer 33

we agree to disagree... I don't want to get more warnings.

Answer 34

The unit circle is blasphemous in this question.

Answer 35

OOOOOOOOOOOOO SNAP!

Answer 36

i'm already banned from community, lul

Answer 37

isn't cos someone said so....

Answer 38

ok so 17//4=4.25 so the biggest multiple of 2pi smaller than 4.25 is 4 so 0.25 is 1/4 but Im looking for the formula to get from pi/4 to sqrt2/2

Answer 39

There is no simple formula for it.

Answer 40

There are ways to calculate it, for sure, but you can't just put it into some simple formula.

Answer 41

thanks everyone