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 ?

- anonymous

- katieb

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- Nnesha

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

- anonymous

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

- Nnesha

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

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## More answers

- Nnesha

r u allowed to use unit circle ?:=)

- anonymous

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

- Nnesha

alright

- Nnesha

|dw:1440591648001:dw|
(x,y) solution where c-coordinate represent cos
and y-coordinate = sin
so what is cos at 7pi/4 ?

- Nnesha

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

- anonymous

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

- anonymous

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

- anonymous

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

- Nnesha

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

- Nnesha

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

- Nnesha

and for example if they ask `what is the exact value of cos(5pi/4)
then cos equal to -sqrt{2} over 2 |dw:1440591987978:dw|

- anonymous

because SACT right ?? thank you so much!!

- anonymous

**ASTC

- Nnesha

ahaha my teacher taught us CAST
which i assume same thing ASTC

- Nnesha

as*

- Nnesha

https://www.youtube.com/watch?v=LE6dmczMc68 here is a video which helps to memorize
but i'll show how to find solution by using 45-45-90 theorem just in case if u don't allowed to use unit circle |dw:1440592694816:dw|
if you understand the first quadrant thats mean you know all quadrants of the unit circle
red liines are increasing by 45 degrees
but the blue one increased by 30 degrees

- Nnesha

and you know radius of the unit circle is one

- Nnesha

|dw:1440592827706:dw|
we need to make right angle on the x-axis (always!)

- Nnesha

|dw:1440592949487:dw|
45-45-90 is an isosceles triangle which means two sides are identical

- anonymous

using pythagoras to find the angles and sides ??

- Nnesha

now you can apply the Pythagorean theorem to find value of x \[\huge\rm a^2+b^2=c^2\] c=hypotenuse
substitute a, b ,c for their values solve for x
you will get the solution thats on the unit circle at 45 degree

- Nnesha

yes right!

- Nnesha

you already know the angles just need to find solutions (x,y) coordinate

- anonymous

awesome thanks! i understand now c: my test is tomorrow hahahahahhahahahahaha

- Nnesha

good luck!

- phi

FYI
\[ \frac{1}{\sqrt{2}}= \frac{2}{\sqrt{2} }\]
(use a calculator to see this, or multiply the first fraction by sqr(2)/sqr(2) )
In the "old days", people really did not like square roots in the denominator (too hard to calculate, I think), so they made a point of rationalizing them.
These days people still do that, but technically it's not wrong to leave the answer 1/sqr(2)

- Nnesha

Well. if you leave the answer as 1/sqrt{2} on the test
i'm pretty sure you will get -1

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