Chapter 6: Trigonometric functions Notes

Sections

1. 6A Trigonometric graphs and modelling Mastered

   Amplitude, period, phase shift and mean value of y = a sin n(x − h) + k, sketching transformed trigonometric graphs, and using trigonometric functions to model periodic situations such as tides.

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2. 6B Differentiating trigonometric functions Mastered

   The derivatives of sin x, cos x and tan x in radians, the chain rule standard forms, and differentiating products, quotients, powers and compositions involving trigonometric functions.

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3. 6C Applications of trigonometric derivatives Mastered

   Tangents and normals to trigonometric curves, finding stationary points and sketching curves such as y = sin x + cos x and y = x + sin x, and optimisation problems involving angles.

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4. 6D Integrating trigonometric functions Mastered

   Standard integrals of sin, cos and sec squared, definite integrals, finding a primitive from an initial condition, the integral of tan x, and the reverse chain rule with trigonometric functions.

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5. 6E Areas with trigonometric functions Mastered

   Finding areas between trigonometric curves and the x-axis, splitting at the x-intercepts, and finding areas between two trigonometric curves.

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6. 6F Proving the derivative of sin x Mastered

   The limit of sin h over h as h tends to zero, proved geometrically, and the proof from first principles that the derivative of sin x is cos x, with the derivatives of cos x and tan x that follow.

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