Simplify sin(180° − θ) and friends

Steps

1. Pretend θ is small (acute). Find which quadrant the angle is in.
2. Use ASTC to decide the sign.
3. 180° ± θ and 360° − θ keep the same function (sin stays sin); 90° ± θ and 270° ± θ swap sin ↔ cos (tan → 1/tan).

For example, sin(180° − θ) = sin θ, cos(180° + θ) = −cos θ, sin(90° + θ) = cos θ.

For the whole topic, read Trigonometry (2-D): key points, common mistakes and how the DSE tests it.

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