Basic Trigonometric Functions

The basic trigonometric functions can be defined in terms of a right triangle. For the angle θ at one apex of the right triangle the functions can be defined by:


Basic triangle geometry

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The Arctangent Problem

In the right triangle shown, the angle can be calculated from

(several notations for the same function.) A common problem which arises in vector addition when the components of the resultant vector are found is that the arctan function in calculators and computer languages cannot distinguish the quadrant of the angle.

Right triangle geometryMore detail on arctan problem
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Arctan Problem Details

Care must be taken when calculating angles from coordinates because of the arctangent problem.

If Rx = and Ry = then θ = °
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