1. **State the problem:** We are given a point (-3, -4) and a radius $r=5$. We need to find the reference angle and the rotational angle for this point. 2. **Recall the formulas:** - The reference angle is the acute angle the terminal side of the point's radius vector makes with the x-axis. - The rotational angle (also called the standard position angle) is the angle measured counterclockwise from the positive x-axis to the point. 3. **Calculate the reference angle:** The reference angle $\theta_{ref}$ can be found using the tangent function: $$\tan(\theta_{ref}) = \left|\frac{y}{x}\right| = \left|\frac{-4}{-3}\right| = \frac{4}{3}$$ 4. **Find $\theta_{ref}$:** $$\theta_{ref} = \arctan\left(\frac{4}{3}\right)$$ Using a calculator or known values: $$\theta_{ref} \approx 53.13^\circ$$ 5. **Determine the quadrant:** The point (-3, -4) lies in the third quadrant (both x and y are negative). 6. **Calculate the rotational angle:** In the third quadrant, the rotational angle $\theta$ is: $$\theta = 180^\circ + \theta_{ref} = 180^\circ + 53.13^\circ = 233.13^\circ$$ 7. **Verify radius:** Given $r=5$, check with Pythagoras: $$(-3)^2 + (-4)^2 = 9 + 16 = 25$$ $$\sqrt{25} = 5$$ This confirms the radius is correct. **Final answers:** - Reference angle $= 53.13^\circ$ - Rotational angle $= 233.13^\circ$