Solve the equation $ ext{cos} rac{30 heta}{9} = rac{1}{2}$, for $ heta ext{ in } ext{ℝ}$, (where $ heta$ is in radians) - Leaving Cert Mathematics - Question 5 - 2010

Looking at the graph:

• The function corresponding to the solid line (continuous) that oscillates between $-1$ and $1$ is $y = h(x) ightarrow x ightarrow ext{cos } 3x$.
• The function corresponding to the dotted line (dashed) that has an amplitude of $2$ is $y = g(x) ightarrow x ightarrow 2 ext{cos } 3x$.
• The function corresponding to the dashed line that oscillates between $-3$ and $3$ is $y = f(x) ightarrow x ightarrow 3 ext{cos } 2x$.

The vertical scale represents the function value ranging from $-3$ to $3$ as the maximum amplitude of $y = f(x)$ is $3$ and the minimum is $-3$.

The horizontal scale should show the intervals for $x$ which corresponds to typical values for the cosine function, such as $0$, rac{ ext{π}}{2}, $ext{π}$, rac{3 ext{π}}{2}, and $2 ext{π}$.