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More work on differentiation with trigonometric functions

More work on differentiation with trigonometric functions

Differentiation of trigonometric functions

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Differentiate $\displaystyle \cos(e^{ax}+bx^2+c)$

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Find an interior angle and length of a diagonal of a random parallelogram.

More work on differentiation with trigonometric functions

The student is given a value of $\cos(\theta)$ and has to find $\theta$.

Shows how to use subexpressions to represent randomly-chosen fractions of $\pi$ and surds, and have them displayed nicely.

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Find $\displaystyle \frac{d}{dx}\left(\frac{m\sin(ax)+n\cos(ax)}{b\sin(ax)+c\cos(ax)}\right)$. Three part question.

More work on differentiation with trigonometric functions

Rearrange some expressions involving logarithms by applying the relation $\log_b(a) = c \iff a = b^c$.

This is a set of practice questions for the non-right-angle trig component of the Australian year 12 Mathematics Standard 2 course.

It asks questions about

• finding sides and angles of right angle triangles,
• finding areas of triangles,
• using the sine rule,
• using the cos rule,
• bearings, and
• radial surveys.

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Differentiate $ (a+bx) ^ {m} \sin(nx)$

Find $\displaystyle \int\frac{ax+b}{(1-x^2)^{1/2}} \;dx$. Solution involves inverse trigonometric functions.