Norbert W. answered • 07/23/16
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a) cos(θ) = 2/5 = 0.4 and x = cos(θ)
The value of y = sin(θ) can be found
from sin2(θ) + cos2(θ) = 1, sin(θ) = ±√(21)/5 ≈ ±0.916
There are two points on the unit circle for which cos(θ) = 2/5
(0.4, -0.916) and (0.4, 0.916)
If an exact value of θ is to be given the best is to represent it
as arccos(2/5) = cos-1(2/5), since its actual value is approximately
66.422° in the first quadrant and 360 - cos-1(2/5) ≈ 293.578°
in the fourth quadrant.
b) In the second quadrant, y = sin(θ) > 0 but x = cos(θ) < 0.
tan(θ) is just not dependent on y.
tan(θ) = sin(θ)/cos(θ) = y/x < 0
Norbert W.
On the unit circle, x = cos(θ) and y = sin(θ).
The equation for the unit circle is x2 + y2 = 1.
This is the same as cos2(θ) + sin2(θ) = 1
y = sin(θ) = ±√(1 - x2)
With the value of x = cos(θ) = 2/5, solve this equation for the value of y.
This is where the value of y =sin(θ) = ±√(21)/5 ≈ ±0.916 comes from
In this problem there is no simple way to find the angle since it is not an angle like 30° or 45°.
Not all angles have simple values for trigonometric functions.
Since cos(θ) = 2/5, have to use inverse of the cosine function to get the
angle. This inverse function is called arc-cosine and on a graphing
calculator is usually represented cos-1. In this case, θ = cos-1(2/5)
Plug this number in and find the angle can be found.
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07/23/16
Alex C.
07/23/16