without using a calculator.
2007-05-20 18:40:59 · 5 answers · asked by Anonymous 1 in Science & Mathematics ➔ Mathematics
cos(45π/4)
= cos(5π/4) because 45π/4 = 11 and 1/4 lots of π which is 10 complete revolutions and then 1 and 1/4 lots of π
cos (5π/4) is in the 3rd quadrant so it is - cos π/4
so cos(45π/4) = - 1/ √2
2007-05-20 18:48:42 · answer #1 · answered by fred 5 · 0⤊ 0⤋
Cosine is a cyclic (repeating) function (graph)
with period 2pi.
So, cos(45pi/4 - 40pi/4) = cos (5pi/4)
(see, we were allowed to do this since 40pi/4 = 10pi which is a multiple of 2pi)
cos (5pi/4) = - cos(pi/4) since 5pi/4 is 180->270 degrees (3rd quadrant).
- cos(pi/4) = -cos(45degrees) = -.707
2007-05-20 18:56:34 · answer #2 · answered by Hk 4 · 0⤊ 0⤋
8pi/4 is just a trip around the unit circle. cos(45pi/4) = cos(37pi/4) = cos (29pi/4) = cos (21pi/4) = cos (13pi/4) = cos (5pi/4) = -(root(2)/2)
2007-05-20 18:48:26 · answer #3 · answered by Bradley B 2 · 0⤊ 0⤋
cosine is periodic with period 2π, so subtract 5(2π) = 10π = 40π/4 from 45π/4 to get 5π/4. then cos(5π/4) = -√2 / 2.
2007-05-20 18:49:00 · answer #4 · answered by Philo 7 · 0⤊ 0⤋
cos(45pi/4)
cos(11pi + (pi/4))
cos(11pi)cos(pi/4) - sin(11pi)sin(pi/4)
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cos(11pi)
cos(10pi + pi)
cos(10pi)cos(pi) - sin(10pi)sin(pi)
keep in mind that 10pi is equivalent to 5 rotations
cos(11pi) = -1
sin(11pi)
sin(10pi + pi)
sin(10pi)cos(pi) + sin(pi)cos(10pi) = 0
cos(11pi)cos(pi/4) - sin(11pi)sin(pi/4)
-cos(pi/4) - 0
-(sqrt(2)/2)
-sqrt(2)/2
cos(11pi)cos(pi/4) - sin(11pi)sin(pi/4) = -sqrt(2)/2
the cos(pi/4) = sqrt(2)/2, cos(pi) = -1, and sin(pi) = 0 is just something you have to remember from previous problems you may have had.
2007-05-20 19:21:18 · answer #5 · answered by Sherman81 6 · 0⤊ 0⤋