Trigonometric Identities (Grade 11 NSC Matric Mathematics): Flashcards

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Trigonometric Identities
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What is a trigonometric identity?

Equation true for all valid angle values

Quotient identity formula

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

When is tan⁡θ\tan \theta undefined?

When cos⁡θ=0\cos \theta = 0 (odd multiples of 90°)

Square/Pythagorean identity

sin⁡2θ+cos⁡2θ=1\sin^2 \theta + \cos^2 \theta = 1

Express sin⁡2θ\sin^2 \theta using cosine

sin⁡2θ=1−cos⁡2θ\sin^2 \theta = 1 - \cos^2 \theta

Express cos⁡2θ\cos^2 \theta using sine

cos⁡2θ=1−sin⁡2θ\cos^2 \theta = 1 - \sin^2 \theta

Main strategy for proving trig identities

Convert everything to sine and cosine

What theorem gives the square identity?

Pythagorean theorem

What appears on tangent graph at restrictions?

Vertical asymptotes

Simplify: tan⁡2θ×cos⁡2θ\tan^2 \theta \times \cos^2 \theta

sin⁡2θ\sin^2 \theta

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