Angles in standard position

An angle in standard position starts at the positive x-axis; its quadrant fixes the sign and its reference angle fixes the size.

A worked example

An angle of 225° lies in quadrant III, where the reference angle is 225 - 180 = 45°, so sin 225° = -0.707.

The mistake people actually make

Sine is negative in quadrants III and IV, cosine in II and III, so a bare calculator value can carry the wrong sign. In an angle-of-elevation question measured from eye level, add the observer's eye height to get the full height.

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