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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:

Recommended:

Category: Math

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

Figures are often enhanced by hand editing; the same results may not be achieved with source sites and source apps.

December 23, 2018

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