Question 278875: Find the smallest number "x" larger than 14pi such that sin x = sqrt2 / 2 (Give exact answer in terms of pi)
Answer by CharlesG2(834)   (Show Source):
You can put this solution on YOUR website! Find the smallest number "x" larger than 14pi such that sin x = sqrt2 / 2 (Give exact answer in terms of pi)
sin x = sqrt(2)/2
x approx 0.78539816
pi approx 3.14
pi/2 approx 1.57
pi/4 approx 0.78539816
x approx pi/4
we need an x larger than 14pi
sin repeats every 2pi
x = pi/4, 2pi + pi/4, 4pi + pi/4, 6pi + pi/4, 8pi + pi/4, 10pi + pi/4,
12pi + pi/4, 14pi + pi/4, ...
smallest x larger than 14 pi is
14pi + pi/4 = 56pi/4 + pi/4 = 57/4 pi
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