why cos(3π/2) = 0
The cosine function is a trigonometric function that represents the ratio of the adjacent side length to the hypotenuse in a right triangle. In a unit circle, where the radius is 1, the x-coordinate of a point on the circle represents the cosine of the corresponding angle.
In the unit circle, the angle corresponding to π/2 radians (or 90 degrees) is at the point (0, 1), where the x-coordinate is 0. As you move clockwise from there, the x-coordinate decreases until you reach the angle 3π/2 radians (or 270 degrees), where the x-coordinate is at its minimum value of -1.
Since cos(3π/2) is equal to the x-coordinate of the point on the unit circle at 3π/2 radians, it is equal to -1.
To understand why cos(3π/2) = 0, we first need to understand what the cosine function represents. The cosine function (cos) is a trigonometric function that calculates the ratio of the adjacent side to the hypotenuse in a right triangle. In other words, it tells us the value of the x-coordinate of an angle on the unit circle.
In trigonometry, angles are usually measured in radians. The angle 3π/2 radians represents an angle in the standard position on the unit circle that starts from the positive x-axis and goes counterclockwise.
In the unit circle, the x-coordinate of a point lying on the unit circle at an angle of 3π/2 radians is 0. This means that cos(3π/2) = 0, because the ratio of the adjacent side to the hypotenuse is zero.
Therefore, cos(3π/2) = 0.