Solving Equations (Grade 12 NSC Matric Mathematics): Flashcards

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Solving Equations
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Period of sine & cosine functions

360°

Period of tangent function

180°

General solution if sin⁡θ=x\sin θ = x

θ=sin⁡−1x+k⋅360°θ = \sin^{-1} x + k·360° or (180°−sin⁡−1x)+k⋅360°(180° - \sin^{-1} x) + k·360°

General solution if cos⁡θ=x\cos θ = x

θ=cos⁡−1x+k⋅360°θ = \cos^{-1} x + k·360° or (360°−cos⁡−1x)+k⋅360°(360° - \cos^{-1} x) + k·360°

General solution if tan⁡θ=x\tan θ = x

θ=tan⁡−1x+k×180°θ = \tan^{-1} x + k × 180°

What does k∈Zk ∈ Z mean in general solutions?

kk is any integer: ..., -2, -1, 0, 1, 2, ...

CAST: Which ratios positive in 1st quadrant (0°-90°)?

All trigonometric ratios

CAST: Which ratio positive in 2nd quadrant (90°-180°)?

Only sine

CAST: Which ratio positive in 3rd quadrant (180°-270°)?

Only tangent

CAST: Which ratio positive in 4th quadrant (270°-360°)?

Only cosine

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