Solution of trigonometric equations (AQA GCSE Further Maths): Flashcards

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Solution of trigonometric equations
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Formula for tan⁡θ\tan \theta using sin and cos

tan⁡θ=sin⁡θcos⁡θ\tan \theta = \frac{\sin \theta}{\cos \theta}

When is tan⁡θ\tan \theta undefined?

At 90°90°, 270°270° (where cos⁡θ=0\cos \theta = 0)

What are asymptotes in tangent graph?

Lines the function approaches but never reaches

Period of tangent function

180°180°

Period of sine and cosine functions

360°360°

What is the principal value?

The first solution your calculator gives

Principal value range for sine

Between −90°-90° and 90°90°

Principal value range for cosine

Between 0°0° and 180°180°

Principal value range for tangent

Between −90°-90° and 90°90°

Second angle formula for sine equations

180°−θ180° - \theta

Second angle formula for cosine equations

360°−θ360° - \theta

Second angle formula for tangent equations

θ+180°\theta + 180°

Calculator mode for trig equations

Degrees mode (look for 'D' or 'DEG')

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