Algebra
# Function Graphs

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).

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.

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

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