A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 one year ago
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
 one year ago
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 ?

This Question is Closed

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.1cos is an even function \[\huge\rm Cos(x)=\cos(x)\] what is cos at 7pi/4 radi ??

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I have no idea, can you explain it to me further. I got pi/4

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.1so how did you get pi/4 ?? :=)

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.1r u allowed to use unit circle ?:=)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0by going around the unit circle a lot ?? yes i am

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.1dw:1440591648001:dw (x,y) solution where ccoordinate represent cos and ycoordinate = sin so what is cos at 7pi/4 ?

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.1and 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
 one year ago
Best ResponseYou've already chosen the best response.0how do i find the value of these coordinates if i am not given the unit circle ??

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0oh! so i just have to make sure there are no square roots at the denominator ??

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0and i will get the coordinates i am looking for? thanks!!

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.1yes right \[\textrm {no square root at the denominator }\]

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.1without looking at the unit circle 2 ways 1) familiar with the 306090 and 454590 triangle 2nd) memorize

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.1and 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
 one year ago
Best ResponseYou've already chosen the best response.0because SACT right ?? thank you so much!!

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.1ahaha my teacher taught us CAST which i assume same thing ASTC

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.1https://www.youtube.com/watch?v=LE6dmczMc68 here is a video which helps to memorize but i'll show how to find solution by using 454590 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
 one year ago
Best ResponseYou've already chosen the best response.1and you know radius of the unit circle is one

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.1dw:1440592827706:dw we need to make right angle on the xaxis (always!)

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.1dw:1440592949487:dw 454590 is an isosceles triangle which means two sides are identical

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0using pythagoras to find the angles and sides ??

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.1now 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
 one year ago
Best ResponseYou've already chosen the best response.1you already know the angles just need to find solutions (x,y) coordinate

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0awesome thanks! i understand now c: my test is tomorrow hahahahahhahahahahaha

phi
 one year ago
Best ResponseYou've already chosen the best response.0FYI \[ \frac{1}{\sqrt{2}}= \frac{2}{\sqrt{2} }\] (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
 one year ago
Best ResponseYou've already chosen the best response.1Well. if you leave the answer as 1/sqrt{2} on the test i'm pretty sure you will get 1
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.