Exploring the Significance of Quadrantal Angles in Trigonometry

Quadrantal Angle

A quadrantal angle is an angle that is formed by the x-axis and a ray originating from the origin on a coordinate plane

A quadrantal angle is an angle that is formed by the x-axis and a ray originating from the origin on a coordinate plane. It has a measure of 90 degrees (π/2 radians) and can be formed in any of the four quadrants.

In the first quadrant, the ray is in the positive x and y direction, forming a 90-degree angle. In the second quadrant, the ray is in the negative x and positive y direction. In the third quadrant, the ray is in the negative x and y direction. And in the fourth quadrant, the ray is in the positive x and negative y direction.

It is important to note that a quadrantal angle lies entirely on one of the axes (either the x-axis or the y-axis) and does not pass through any other quadrants.

Quadrantal angles have a special significance in trigonometry because their sine, cosine, and tangent values are well-defined and often used to solve mathematical problems. For example, when dealing with quadrantal angles, the sine and tangent functions are either 1 or -1, while the cosine function is either 0 or -0, depending on the quadrant in which the angle is located.

Overall, understanding quadrantal angles is fundamental in trigonometry as they help in solving equations, graphing functions, and analyzing geometric shapes on the coordinate plane.

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