## 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 ?

1. Nnesha

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

2. anonymous

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

3. Nnesha

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

4. Nnesha

r u allowed to use unit circle ?:=)

5. anonymous

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

6. Nnesha

alright

7. Nnesha

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

8. 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

9. anonymous

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

10. anonymous

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

11. anonymous

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

12. Nnesha

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

13. Nnesha

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

14. 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|

15. anonymous

because SACT right ?? thank you so much!!

16. anonymous

**ASTC

17. Nnesha

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

18. Nnesha

as*

19. 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

20. Nnesha

and you know radius of the unit circle is one

21. Nnesha

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

22. Nnesha

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

23. anonymous

using pythagoras to find the angles and sides ??

24. 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

25. Nnesha

yes right!

26. Nnesha

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

27. anonymous

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

28. Nnesha

good luck!

29. 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)

30. Nnesha

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