Mathematics: Simplify tan(-x)/sin(-x) a sec x b cos x c -sec x d-cos x

Simplify tan(-x)/sin(-x) a sec x b cos x c -sec x

Shaynele

08.07.2020

The shape of the graph is sinusoidal

The domain is from θ = -∞ to +∞

The range is from r = 2 to -2

The maximum r value of the graph is r = 2

The graph is continuous and bounded with symmetry about the line origin and the y-axis

The graph has no asymptotes

Step-by-step explanation:

The graph r = -2·cos(5θ) and table of values are attached

The maximum r can be found by differentiating the function as follows;

$\frac{\mathrm{d} r}{\mathrm{d} \theta } = \frac{\mathrm{d} \left (-2cos5 \theta \right )}{\mathrm{d} \theta } = 0$

$\therefore 10 \cdot sin(5\cdot x)= 0\\$

sin(5·θ) = 0, hence the maximum value occurs at θ = 0 or θ = π

Which gives, r = -2 and 2. Therefore, maximum r = 2 and minimum r = -2.

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