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Graphs are visual representations of functions. If you know how to read graphs, you can say a lot about a function just by looking at its graph. Learn this fine art of mathematical divining.

Given the equation \(4x^2+2\sqrt{3}xy+2y^2=1\).

Through what angles \(\theta \in [0,\pi]\) should the axes be rotated so that the term \(xy\) is removed from the transformed equation?

Give the answer as the sum of all values of \(\theta\)(in degrees).

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Finding the area of the figure created by \(x^2+y^2=1\) is too easy.

The graph above shows the figure created by the function \(x^2+(y+x)^2=1\).

Find the area of this tilted ellipse correct to 2 decimal places.

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If \(f(x) \) and \( g(x) \) have the same fundamental period, then so does \( f(x) + g(x) \).

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