find cos pi/4 without using a calculator.

Question

amistre64 · Answer

you would have to know what the right triangle for pi/4 looks like

anonymous · Answer

sqrt 2/2

amistre64 · Answer

pi = 180 when converting radians to degrees

pi/4 radians = 180/4 degrees = 45 degrees

amistre64 · Answer

a 45 degree angled right triangle can be fashioned out of a square that is cut diagonally in half

amistre64 · Answer

since a square has all sides equal; each leg of the rt trianlge is the same

amistre64 · Answer

to find the diagonal we can use the pythag thrm such that:

s^2 + s^2 = diag^2

2s^2 = diag^2

diag = sqrt(2s^2) = (s)sqrt(2)

when the sides = 1 it is quite easy to see that the diag = sqrt(2)

amistre64 · Answer

now cosine is defined as the adjacent side over the hypotenuse; lets use the easy measurement of 1 for each side then;  cos(45) = 1/sqrt(2)

which can be reshaped into:  sqrt(2)/2 if need be for those sticklers out there who want to say that radicals dont belong in the bottom of a fraction :)

anonymous · Answer

amistre64, are you calling me a stickler? lol

amistre64 · Answer

like a cactus ;)