Trigonometric Equations (HSC SSCE Mathematics Advanced): Quizzes

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Trigonometric Equations
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What is a trigonometric equation?

Equation with sin, cos, or tan functions

Why is a restricted domain like [0°,360°][0°, 360°] typically chosen?

To capture one complete cycle

What is the interval for the principal angle?

[0°,360°][0°, 360°]

According to the CAST rule, which functions are positive in Quadrant 2?

Only sin⁡θ\sin \theta

If cos⁡θ\cos \theta is positive, in which quadrants are the solutions?

Quadrants 1 and 4

How often does tan⁡θ\tan \theta repeat its values?

Every 180°180° (or π\pi radians)

What is the principal angle when solving cos⁡θ=0.5\cos \theta = 0.5?

60°60°

To solve equations in extended domains like [0°,720°][0°, 720°], what should you do first?

Find all solutions in [0°,360°][0°, 360°]

What is the first step to solve 2sin⁡2θ−sin⁡θ−1=02\sin^2\theta - \sin\theta - 1 = 0?

Substitute u=sin⁡θu = \sin\theta

Why should you verify solutions by substituting back into the original equation?

To confirm solutions and catch errors

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