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The image you provided contains mathematical problems related to trigonometric equations. Let's break down each of them:

### 1. **Find the solution set for each of the following equations:**

#### (a) \( \sin x = \sin 350^\circ \) for \( 0^\circ \leq x \leq 360^\circ \)

Since \( \sin \theta \) has the property that \( \sin \theta = \sin (180^\circ - \theta) \), we find:

- \( \sin 350^\circ \) is equivalent to \( \sin (-10^\circ) \), which means the solutions for \( x \) will occur when \( x = 360^\circ - 350^\circ = 10^\circ \).

Thus, \( x = 10^\circ \) and any other angle within \( 0^\circ \leq x \leq 360^\circ \).

#### (b) \( \sin (x - 40^\circ) = \sin 110^\circ \) for \( 0^\circ \leq x \leq 360^\circ \)

This can be solved by using the identity \( \sin A = \sin B \), leading to:
- \( x - 40^\circ = 110^\circ \)
- \( x - 40^\circ = 180^\circ - 110^\circ \)

#### (c) \( \cos (3x + 48^\circ) = \cos 75^\circ \) for \( 0^\circ \leq x \leq 180^\circ \)

Use the property \( \cos A = \cos B \), which implies:
- \( 3x + 48^\circ = 75^\circ \)
- \( 3x + 48^\circ = 360^\circ - 75^\circ \)

#### (d) \( \cos \left( \frac{3}{2}x - 36^\circ \right) = \cos 264^\circ \) for \( 0^\circ \leq x \leq 360^\circ \)

#### (e) \( \tan (x - 20^\circ) = \tan 320^\circ \) for \( 0^\circ \leq x \leq 360^\circ \)

### 2. **Solve the equation \( \sqrt{3} \cos x + \sin x = 2 \cos 25^\circ \) for \( 0^\circ \leq x \leq 360^\circ \)**

I can guide you through the steps for each if you'd like. Do you need detailed step-by-step solutions for any particular part?

### Follow-Up Questions:

1. What is the general solution for trigonometric equations involving sine and cosine?
2. How do you use the unit circle to determine the solution for sine or cosine functions?
3. How does the period of trigonometric functions affect the solution to equations like these?
4. What transformations can be applied to trigonometric functions to simplify equations?
5. Can you explain how to use inverse trigonometric functions to solve for angles?

**Tip:** For trigonometric equations, always consider the symmetry of the functions and their periodic nature when finding all possible solutions.

Find the solution set for each of the given trigonometric equations within specified intervals.

Learn how to solve various trigonometric equations involving sine, cosine, and tangent functions. This lesson covers key trigonometric properties and provides a step-by-step solution for equations within specified intervals, suitable for students in Grades 10-12.

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