Cos(3π/2)
In mathematics, cosine (abbreviated as cos) is a trigonometric function that relates the angle of a right triangle to the ratio between the length of the adjacent side and the hypotenuse
In mathematics, cosine (abbreviated as cos) is a trigonometric function that relates the angle of a right triangle to the ratio between the length of the adjacent side and the hypotenuse. It is defined as the ratio of the adjacent side of a right triangle to its hypotenuse.
Cos(3π/2) refers to the cosine function evaluated at an angle of 3π/2 radians. We can first express 3π/2 in degrees, because we are more familiar with degrees in everyday life. To convert radians to degrees, we use the conversion factor 180/π.
3π/2 radians * (180/π degrees/radians) = 270 degrees
So, Cos(3π/2) is equal to the cosine of the angle 270 degrees. In a unit circle, 270 degrees is located in the third quadrant, where the cosine function is negative.
In the third quadrant of a unit circle, the x-coordinate is negative (adjacent side) and the y-coordinate is negative (hypotenuse). The cosine function can be written as cos(θ) = x/h, where x is the adjacent side and h is the hypotenuse.
Since we are in the third quadrant, the hypotenuse is negative and equal to -1, and the adjacent side is also negative and equal to 0. So, the cosine of 3π/2 (270 degrees) is:
cos(3π/2) = x/h = 0/-1 = 0
Therefore, Cos(3π/2) equals 0.
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