## Determine Trigonometric Functions with Given Conditions

## Problem 651

**(a) **Find a function

\[g(\theta) = a \cos(\theta) + b \cos(2 \theta) + c \cos(3 \theta)\]
such that $g(0) = g(\pi/2) = g(\pi) = 0$, where $a, b, c$ are constants.

**(b)** Find real numbers $a, b, c$ such that the function

\[g(\theta) = a \cos(\theta) + b \cos(2 \theta) + c \cos(3 \theta)\]
satisfies $g(0) = 3$, $g(\pi/2) = 1$, and $g(\pi) = -5$.