Draw the graph of y = 3 x + 2 x for 0^ x 360^ and use it to solve 3 x + 2 x = 0.

Let's continue with parts 7b and 7c.

7b. Draw a graph of the relation $y = 3\sin x + 2\cos x$ for $0^\circ \le x \le 360^\circ$.

Step 1: Set up the axes.
Draw a horizontal x-axis for angles from $0^\circ$ to $360^\circ$ and a vertical y-axis for the values of $y$.

Step 2: Apply the given scales.

• On the x-axis, mark intervals such that $2\text{ cm}$ represents $30^\circ$. This means $1\text{ cm}$ represents $15^\circ$.
• On the y-axis, mark intervals such that $2\text{ cm}$ represents $1\text{ unit}$. This means $1\text{ cm}$ represents $0.5\text{ units}$. Ensure the y-axis covers the range of $y$ values from the table (approximately -4 to 4).

Step 3: Plot the points from the completed table (from 7a).
Plot the following $(x, y)$ points:
$(0^\circ, 2.0)$, $(30^\circ, 3.2)$, $(60^\circ, 3.6)$, $(90^\circ, 3.0)$, $(120^\circ, 1.6)$, $(150^\circ, -0.2)$, $(180^\circ, -2.0)$, $(210^\circ, -3.2)$, $(240^\circ, -3.6)$, $(270^\circ, -3.0)$, $(300^\circ, -1.6)$, $(330^\circ, 0.2)$, $(360^\circ, 2.0)$.

Step 4: Draw a smooth curve.
Connect the plotted points with a smooth curve to represent the graph of $y = 3\sin x + 2\cos x$.

7c. Use the graph to solve: