CAST: which ones are positive
Going round from quadrant I: All are positive, then only Sin, then only Tan, then only Cos. Find the reference angle, use the 0°–90° value, then give it the sign of its quadrant.
Drag the point round the circle. sin θ, cos θ and tan θ change on the circle and on their graphs at the same time, with exact values for the special angles.
Drag along the graph to move the angle. The height of the sin curve is the red leg on the circle; the cos curve follows the blue leg.
Every other special angle uses these five columns, with a + or − sign from its quadrant.
| sin | 0 | 12 | √22 | √32 | 1 |
|---|---|---|---|---|---|
| cos | 1 | √32 | √22 | 12 | 0 |
| tan | 0 | √33 | 1 | √3 | — |
Going round from quadrant I: All are positive, then only Sin, then only Tan, then only Cos. Find the reference angle, use the 0°–90° value, then give it the sign of its quadrant.
A full turn is 360° or 2π radians, so 180° = π. To change degrees to radians multiply by π/180; to go back multiply by 180/π.
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