Trigonometric Equations (HSC SSCE Mathematics Advanced): Flashcards

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Trigonometric Equations
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Trigonometric equation definition

Equation with trig functions like sin, cos, or tan

Principal angle definition

Angle anticlockwise from +ve xx-axis in [0°,360°][0°, 360°]

CAST rule: Quadrant 1 (A)

All trig ratios positive

CAST rule: Quadrant 2 (S)

Only sin⁡θ\sin \theta positive

CAST rule: Quadrant 3 (T)

Only tan⁡θ\tan \theta positive

CAST rule: Quadrant 4 (C)

Only cos⁡θ\cos \theta positive

Period of sin⁡θ\sin \theta and cos⁡θ\cos \theta

360°360° (or 2π2\pi radians)

Period of tan⁡θ\tan \theta

180°180° (or π\pi radians)

Quadrants where sin⁡θ\sin \theta is positive

Quadrants 1 and 2

First step for quadratic trig equations

Substitute variable (e.g., u=sin⁡θu = \sin\theta)

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