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Angles in standard position and the CAST rule

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Useful for: MCR3U IB Math AA SL & HL AP® Precalculus

Learn it An angle in standard position starts on the positive x-axis and turns counterclockwise. The reference angle is the acute angle to the x-axis. CAST tells which ratios are positive: quadrant 1 All, 2 Sine, 3 Tangent, 4 Cosine.

Example: Is cos 220° positive or negative?

  1. 220° is in quadrant 3 (between 180° and 270°).
  2. Only tangent is positive there, so cos 220° is negative.
  3. Reference angle 220° − 180° = 40°: cos 220° = −cos 40°.

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