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Remedial Trigonometry

Limits

A few limits are necessary to prove or follow calculus formulas involving trig functions.

sinθ/θ

{$$ {\lim_{\theta\rightarrow0} {\frac{\sin\theta}{\theta}} = 1} $$}

A geometric proof based on the pinching theorem is here.

(cosθ - 1)/θ

{$$ \lim_{\theta\rightarrow0} {\frac{\cos\theta - 1}{\theta}} = 0 $$}

Depends on the above, demonstrated here

Trig Identities

Pythagorean

{$$ \sin^2\alpha + \cos^2\alpha = 1 $$}

{$$ \tan^2\alpha + 1 = \sec^2\alpha $$}

Sine of Sums

{$$ \sin(\alpha + \beta ) = \sin(\alpha)\cos(\beta) + \cos(\alpha)\sin(\beta) $$}

Cosine of Sums

{$$ \cos(\alpha + \beta ) = \cos(\alpha)\cos(\beta)-\sin(\alpha)\sin(\beta) $$}


Sources:

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Category: Math

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This is a student's notebook. I am not responsible if you copy it for homework, and it turns out to be wrong.

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August 05, 2017

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