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I have displayed the image you uploaded. I will now help you solve parts A, B, C, and D of the assessment.

### A. True/False Questions:
1. **True** - Sine is the ratio of the opposite side and the hypotenuse in a right triangle.
2. **False** - The reciprocal of cosine is secant, not sine.
3. **False** - In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the two legs (Pythagorean theorem), not the difference.
4. **True** - If \(\tan \theta = \frac{6}{8}\), then \(\cot \theta = \frac{8}{6}\).
5. **False** - Cosecant is defined as the ratio of the hypotenuse to the opposite side, not the other way around.
6. **True** - Tangent is the reciprocal of cotangent.
7. **True** - If \(\sec \theta = 1\), then \(\cos \theta\) is also 1 because secant is the reciprocal of cosine.
8. **True** - This is the Pythagorean theorem.
9. **False** - If \(\cos \theta = \frac{8}{6}\), it would be incorrect to say the adjacent side length is 6 (this depends on the unit circle or triangle dimensions).
10. **True** - If two functions are reciprocals, their product equals 1.

### B. Trigonometric Values (nearest thousandths):
1. \(\sin 36^\circ \approx 0.588\)
2. \(\tan -110^\circ \approx 0.364\)
3. \(\cot -125^\circ \approx 0.466\)
4. \(\cos 105^\circ \approx -0.259\)
5. \(\csc 50^\circ \approx 1.305\)
6. \(\sec 40^\circ \approx 1.305\)

### C. Find the value of \(\theta\):
1. \(\sin \theta = 0.319\), \(\theta \approx 18.59^\circ\)
2. \(\tan \theta = -0.839\), \(\theta \approx -39.36^\circ\)
3. \(\cos \theta = 0.087\), \(\theta \approx 85.02^\circ\)

### D. Solving the Triangle (Given \(m\angle A = 50^\circ\) and side \(a = 9 \text{ cm}\)):
To find \(m\angle B\), \(b\), and \(c\):
- \(m\angle B = 90^\circ - 50^\circ = 40^\circ\)
- Using sine and cosine ratios:
  \[
  b = a \cdot \tan(50^\circ) \approx 9 \cdot 1.1918 = 10.73 \text{ cm}
  \]
  \[
  c = \frac{9}{\cos(50^\circ)} \approx \frac{9}{0.6428} = 14.00 \text{ cm}
  \]

Would you like further details on any of the steps or have additional questions?

Here are 5 follow-up questions:
1. How is the reciprocal of a trigonometric function determined?
2. Can you explain how to calculate cotangent from tangent?
3. What is the importance of the Pythagorean theorem in trigonometry?
4. Why is the product of reciprocal functions equal to 1?
5. How do we determine angles and sides of a right triangle using trigonometric ratios?

**Tip:** When solving trigonometric problems, always ensure your calculator is in the correct mode (degrees or radians) to avoid calculation errors.

Answer Letter A, B, C and D from the trigonometry assessment.

Solve true/false questions and calculate trigonometric values, including sine, cosine, and tangent functions. Apply the Pythagorean theorem to find unknown sides and angles in a right triangle. Suitable for students in Grades 9-11.

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