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I see you’ve uploaded a photo of a mathematics unit test. Let's break down the sections and solve a few problems from each.

### SECTION A:
#### Q.1) **Determine which of the following pairs of angles are co-terminal.**
- Co-terminal angles differ by a multiple of \( 360^\circ \). We check each option:
  - a) \( 420^\circ - (-300^\circ) = 720^\circ = 2 \times 360^\circ \) → co-terminal
  - b) \( 330^\circ - (-45^\circ) = 375^\circ \) → not co-terminal
  - c) \( 330^\circ - (-60^\circ) = 390^\circ \) → not co-terminal
  - d) \( 1230^\circ - 930^\circ = 300^\circ \) → not co-terminal

**Answer: a) \( 420^\circ \), \( -300^\circ \)**.

#### Q.2) **If \( 5\tan \theta = 4 \), then \( \frac{5 \sin \theta - 3 \cos \theta}{5 \sin \theta + 2 \cos \theta} \)**
We know that \( \tan \theta = \frac{\sin \theta}{\cos \theta} \), so \( \frac{5 \sin \theta}{\cos \theta} = 4 \), giving us relationships between \( \sin \theta \) and \( \cos \theta \). Substituting and simplifying will give the answer, which needs further steps.

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### SECTION B:
#### Q.3) **In \( \Delta ABC \), if \( m \angle A = \frac{7\pi}{36} \), \( m \angle B = 120^\circ \), find \( m \angle C \) in degrees and radians.**
We know that the sum of angles in a triangle is \( 180^\circ \). So, 
\[ m \angle C = 180^\circ - 120^\circ - \frac{7\pi}{36} \times \frac{180^\circ}{\pi} \]
Simplifying this gives \( m \angle C \).

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### SECTION C:
#### Q.9) **Find the other trigonometric functions if \( \sec \theta = -3 \) and \( \pi < \theta < \frac{3\pi}{2} \).**
We know:
- \( \sec \theta = \frac{1}{\cos \theta} \), so \( \cos \theta = -\frac{1}{3} \).
Now, we can calculate \( \sin \theta \), \( \tan \theta \), \( \csc \theta \), \( \cot \theta \), knowing the quadrant of \( \theta \).

Would you like detailed solutions for any specific questions?

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Here are 5 questions to expand upon:
1. What are the steps to find the modulus and amplitude of a complex number?
2. How do you convert radians to degrees and vice versa?
3. How do co-terminal angles work and what is their geometric significance?
4. What is the polar form of complex numbers and how do you find polar coordinates?
5. How do you solve trigonometric identities involving multiple angles?

**Tip**: When solving for unknown angles or values in triangles, always make sure to verify the sum of angles equals \( 180^\circ \).

Determine which of the following pairs of angles are co-terminal. If 5tanθ = 4, then solve for the expression.

Explore how to determine co-terminal angles and solve trigonometric expressions for Class XI students. Understand the concepts behind co-terminal angles and the relationship between trigonometric functions such as tan(θ), sin(θ), and cos(θ).

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