It seems like you have a mix of angle evaluations (like sine and cosine) and points for which you'd like to find the sine and cosine using the definitions. I'll break down the questions and also generate the corresponding images where requested.

Let's begin with the angle-based evaluations:

1. sin(250°)
2. sin(320°)
3. cos(140°)
4. cos(200°)
5. cos(300°)
6. sin(120°)

For these, I will calculate the values and also produce images for any that you requested. I'll start by working on the values and the corresponding images.

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For Problems 7–14, using points to find sin(θ) and cos(θ):

Using the definitions of sine and cosine from a point $(x, y)$ on the terminal side of the angle:

• $r = \sqrt{x^2 + y^2}$
• $\sin(\theta) = \frac{y}{r}$
• $\cos(\theta) = \frac{x}{r}$

I will proceed with solving for each of the points provided and generate any images needed.

Let me process the calculations and generate the required images! math

Function to calculate sin and cos for a point (x, y)

def calculate_sin_cos(x, y): r = math.sqrt(x2 + y2) sin_theta = y / r cos_theta = x / r return r, sin_theta, cos_theta

Points given

points = [(7, 11), (4, 1), (-2, 5), (-6, 9), (4, -8), (8, -3), (-24, -7), (-3, -4)]

Calculate sin and cos for each point

results = [] for point in points: r, sin_theta, cos_theta = calculate_sin_cos(point[0], point[1]) results.append((point, r, sin_theta, cos_theta))

resultsHere are the results for the sine and cosine calculations based on the points you provided:

1. Point (7, 11)

   • $r = 13.04$
   • $\sin(\theta) = 0.844$
   • $\cos(\theta) = 0.537$

2. Point (4, 1)

   • $r = 4.12$
   • $\sin(\theta) = 0.243$
   • $\cos(\theta) = 0.970$

3. Point (-2, 5)

   • $r = 5.39$
   • $\sin(\theta) = 0.928$
   • $\cos(\theta) = -0.371$

4. Point (-6, 9)

   • $r = 10.82$
   • $\sin(\theta) = 0.832$
   • $\cos(\theta) = -0.555$

5. Point (4, -8)

   • $r = 8.94$
   • $\sin(\theta) = -0.894$
   • $\cos(\theta) = 0.447$

6. Point (8, -3)

   • $r = 8.54$
   • $\sin(\theta) = -0.351$
   • $\cos(\theta) = 0.936$

7. Point (-24, -7)

   • $r = 25.00$
   • $\sin(\theta) = -0.280$
   • $\cos(\theta) = -0.960$

8. Point (-3, -4)