anonymous
  • anonymous
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 ?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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Nnesha
  • Nnesha
cos is an even function \[\huge\rm Cos(-x)=\cos(x)\] what is cos at 7pi/4 radi ??
anonymous
  • anonymous
I have no idea, can you explain it to me further. I got pi/4
Nnesha
  • Nnesha
so how did you get pi/4 ?? :=)

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Nnesha
  • Nnesha
r u allowed to use unit circle ?:=)
anonymous
  • anonymous
by going around the unit circle a lot ?? yes i am
Nnesha
  • Nnesha
alright
Nnesha
  • Nnesha
|dw:1440591648001:dw| (x,y) solution where c-coordinate represent cos and y-coordinate = sin so what is cos at 7pi/4 ?
Nnesha
  • 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
  • anonymous
how do i find the value of these coordinates if i am not given the unit circle ??
anonymous
  • anonymous
oh! so i just have to make sure there are no square roots at the denominator ??
anonymous
  • anonymous
and i will get the coordinates i am looking for? thanks!!
Nnesha
  • Nnesha
yes right \[\textrm {no square root at the denominator }\]
Nnesha
  • Nnesha
without looking at the unit circle 2 ways 1) familiar with the 30-60-90 and 45-45-90 triangle 2nd) memorize
Nnesha
  • 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
  • anonymous
because SACT right ?? thank you so much!!
anonymous
  • anonymous
**ASTC
Nnesha
  • Nnesha
ahaha my teacher taught us CAST which i assume same thing ASTC
Nnesha
  • Nnesha
as*
Nnesha
  • 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
  • Nnesha
and you know radius of the unit circle is one
Nnesha
  • Nnesha
|dw:1440592827706:dw| we need to make right angle on the x-axis (always!)
Nnesha
  • Nnesha
|dw:1440592949487:dw| 45-45-90 is an isosceles triangle which means two sides are identical
anonymous
  • anonymous
using pythagoras to find the angles and sides ??
Nnesha
  • 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
  • Nnesha
yes right!
Nnesha
  • Nnesha
you already know the angles just need to find solutions (x,y) coordinate
anonymous
  • anonymous
awesome thanks! i understand now c: my test is tomorrow hahahahahhahahahahaha
Nnesha
  • Nnesha
good luck!
phi
  • 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
  • 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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