Calculate Angles of Quadrants
Calculator for the span of the angles in degrees and radian of the four quadrants. Also, the algebraic sign of the trigonimetric values, sine, cosine, tangent and cotangent will be shown. Please select one quadrant to get the values.
The plane is divided into quadrants by two mutually perpendicular coordinate axes. The term quadrant comes from the Latin word quadrans (quarter) and denotes one quarter of a complete rotation around the origin. Starting with the positive x-axis, the quadrants are numbered from 1 to 4 in the mathematically positive direction of rotation, i.e., counterclockwise.
Each quadrant encompasses an angular range of 90 degrees in angular measure, corresponding to an interval of length π/2 in radians.
The signs of trigonometric functions are determined by the angle's position in the coordinate system. The sine corresponds to the y-coordinate, and the cosine to the x-coordinate of a point on the unit circle. Tangent and cotangent are the quotients of these values and inherit their sign dependencies. The signs of tangent and cotangent are always the same for a given angle.
Knowing the quadrant allows to determine the signs of trigonometric functions even without specific angle values.
In the first quadrant, all coordinates are positive, therefore sine, cosine, tangent, and cotangent are positive.
In the second quadrant, the x-coordinate is negative and the y-coordinate is positive, therefore the sine is positive and the cosine is negative. So, the tangent and cotangent are negative.
In the third quadrant, both the x- and y-coordinates are negative, so the sine and cosine are negative, while the tangent and cotangent become positive.
In the fourth quadrant, the x-coordinate is positive and the y-coordinate is negative, making the cosine positive, the sine negative, and therefore also the tangent and cotangent negative.