Saturday, November 3, 2012
Practice problems for Homework 10
Find the high point and low point surrounding the median point closest to (0, 0) for the following trig functions.
f(x) = 6sinx - 8cosx
g(x) = 2sinx - 4cosx
Here are three points on the unit circle in the complex plane. Multiplying two points of the form costheta + isintheta and cosiota+isiniota gives us the values for the angle theta + iota.
a = 1/5 + i2sqrt(6)/5
b = 2/5 + isqrt(21)/5
ab =
a² =
a³ =
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f(x) = 6sinx - 8cosx
ReplyDelete6² + 8² = 100, so the amplitude is 10
when x = arctan(4/3) the function = 0 so arctan(4/3) = .927295... or .2952pi
f(x) = 10sin(x -.2952pi)
median (.2952pi, 0)
high point (.7952pi, 10)
low point (-.2048pi, -10)
g(x) = 2sinx - 4cosx
sqrt(2² + 4²) = sqrt(20) = 2sqrt(5)
2sinx - 4cosx = 0
2sinx = 4cosx
2tanx = 4
tanx = 2
arctan(2) = .3524pi
g(x) = 2sqrt(5)sin(x - .3524pi)
median (.3524pi, 0)
high point (.8524pi, 2sqrt(5))
low point (-.1476pi, -2sqrt(5))
Here are three points on the unit circle in the complex plane. Multiplying two points of the form costheta + isintheta and cosiota+isiniota gives us the values for the angle theta + iota.
a = 1/5 + i2sqrt(6)/5
b = 2/5 + isqrt(21)/5
ab = 2/25 - 6sqrt(14)/25 + i((sqrt(21)+4sqrt(6))/25
a² = -23/25 + i4sqrt(6)/25
a³ = -71/125 - i42sqrt(6)/125