Quadrantal Angles Calculator Online

The Quadrantal Angles Calculator is an essential tool for students and professionals alike. It provides quick and accurate trigonometric values for angles that are either 0, 90, 180, or 270 degrees. This functionality is particularly useful as these angles, being on the axes, have trigonometric values that are often needed in calculations but can be cumbersome to remember.

Formula of Quadrantal Angles Calculator

Understanding the formulae for calculating trigonometric values at quadrantal angles is key to using the calculator effectively. Here are the formulas:

• For an angle θ in standard position:
  • If θ lies on the positive x-axis (0 degrees or 360 degrees):
    • sin(θ) = 0, cos(θ) = 1, tan(θ) = 0
  • If θ lies on the positive y-axis (90 degrees):
    • sin(θ) = 1, cos(θ) = 0, tan(θ) = undefined
  • If θ lies on the negative x-axis (180 degrees):
    • sin(θ) = 0, cos(θ) = -1, tan(θ) = 0
  • If θ lies on the negative y-axis (270 degrees):
    • sin(θ) = -1, cos(θ) = 0, tan(θ) = undefined

Useful Table for Quick Reference

To assist with quick calculations, here is a table that summarizes the trigonometric values for the quadrantal angles:

Angle (Degrees)	Sin	Cos	Tan
0 or 360	0	1	0
90	1	0	Undefined
180	0	-1	0
270	-1	0	Undefined

This table serves as a handy reference to avoid the need for manual calculations.

Examples of Quadrantal Angles Calculator

To illustrate how to use the Quadrantal Angles Calculator, consider the following example: Calculate the sine, cosine, and tangent for an angle of 90 degrees. By referring to our table or using the calculator directly, we find that sin(90) = 1, cos(90) = 0, and tan(90) = undefined.

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