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 $f(x) + g(x)$.