Question

Find the exact value of cos 11π/4

Answer 1

Now pi/4 = 180/4 = 45 degrees.

So we want to find cos of 45x11 = 495 .


So are you aware that every 180 degrees the value of cos equals cos 0 and becomes 1?

Answer 2

no :S

but I am now

Answer 3

ok sorry its 360 degrees; nt 180. :P

Every 360 degrees 1 complete rotation is done; so cos 360 = cos 0 actually.

So we're left with the other 495-360 = cos 135.

If you want to know, then cos x = cos(180-x)

=> cos 135 = cos(180-135)

=> cos 135 = cos 45.

However the angle of 135 lies in the II quadrant where cos is negative.

So cos 45 = 1/ sqrt 2, however cos 135 will be -1/sqrt 2

also, cos 135 = cos of 3pi/4. = -1/sqrt 2

Answer 4

got it! thanks :)

Answer 5

alternatively, could i do this?

11π/4 = 12π/4 - π/4
= 3π - π/4
= 2π + π - π/4
2π = 0 (2π is one complete revolution)
therfore, 11π/4 = π - π/4
in the 2nd quadrant, angles are in the form π-theta, so the angle is in the 2nd quadrant, and cos theta is neg in the 2nd quadrant
therfore, cos 11π/4 = cos (π- π/4)
= - cos π/4
= - 1/ sqrt 2

Answer 6

the last step you did it in radians i did it in degrees. but yeah thats fine. :)

Answer 7

ok, thanks