Π/2 Radians: The Equivalent Of 90 Degrees And Its Trigonometric Significance

3π/2 radians

270°

3π/2 radians is an angle measure that represents three halves of a full circle in the counter-clockwise direction. To understand this better, we can break down the process of measuring angles in radians.

In a unit circle, the circumference is 2π. Hence, 2π/2 or π radians is one-half the circle, and 2π or 4π/2 radians is equal to a full circle.

Therefore, 3π/2 radians is equal to (3/2) times the circumference of the unit circle in the counter-clockwise direction, starting from the positive x-axis.

To visualize 3π/2 radians, imagine a unit circle with its center at the origin, that is, a circle with a radius of 1. Starting from the positive x-axis, go in the counter-clockwise direction for three-quarters of the circle, or 270 degrees. This will result in reaching the negative y-axis.

In other words, the terminal side of 3π/2 radians lies on the negative y-axis.

Graphically, it can be represented as:


In this circle diagram, 3π/2 radians is shown as the angle between the positive x-axis and the negative y-axis.

More Answers: