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The image you uploaded presents a trigonometry problem asking for the conversion of trigonometric ratios of non-acute angles into corresponding ratios for acute angles. Let's break down how to approach this type of problem.

### For each angle, we need to:
1. **Identify the quadrant** in which the angle lies (since trigonometric functions change signs based on the quadrant).
2. **Use reference angles**, which are the acute angles that the given angles relate to, and apply the proper sign based on the quadrant.
3. **Express the trigonometric function of the given angle** in terms of an acute angle.

I'll start with the first few parts and explain the general method.

#### a. \( \sin 197^\circ \)
- **Quadrant:** \( 197^\circ \) lies in the third quadrant (between 180° and 270°).
- **Reference angle:** \( 197^\circ - 180^\circ = 17^\circ \).
- **Sign:** In the third quadrant, sine is negative.
- **Result:** \( \sin 197^\circ = -\sin 17^\circ \).

#### b. \( \cos 245^\circ \)
- **Quadrant:** \( 245^\circ \) lies in the third quadrant.
- **Reference angle:** \( 245^\circ - 180^\circ = 65^\circ \).
- **Sign:** In the third quadrant, cosine is negative.
- **Result:** \( \cos 245^\circ = -\cos 65^\circ \).

#### c. \( \csc 234^\circ \)
- **Quadrant:** \( 234^\circ \) lies in the third quadrant.
- **Reference angle:** \( 234^\circ - 180^\circ = 54^\circ \).
- **Sign:** In the third quadrant, cosecant (reciprocal of sine) is negative.
- **Result:** \( \csc 234^\circ = -\csc 54^\circ \).

#### d. \( \sec 259^\circ \)
- **Quadrant:** \( 259^\circ \) is also in the third quadrant.
- **Reference angle:** \( 259^\circ - 180^\circ = 79^\circ \).
- **Sign:** In the third quadrant, secant (reciprocal of cosine) is negative.
- **Result:** \( \sec 259^\circ = -\sec 79^\circ \).

Would you like me to continue with the remaining parts of the problem or elaborate further on any of these steps?

### Here are some related questions to consider:
1. How do we find the reference angle for any trigonometric function?
2. How do the signs of trigonometric functions vary across different quadrants?
3. Why does the reference angle only depend on the nearest axis (either 180° or 360°)?
4. What is the significance of using trigonometric identities in simplifying angles?
5. Can trigonometric functions of angles greater than 360° also be reduced similarly?

**Tip:** Always remember the ASTC rule (All Students Take Calculus), which helps you determine which functions are positive in which quadrant.

Nyatakan perbandingan trigonometri berikut ini ke dalam perbandingan trigonometri sudut lancip: sin 197°, cos 245°, cosec 234°, sec 259°, tan 274°, cos 253°, tan 212°, sin 253°, sec 222°, tan 281°, sec 278°, cosec 191°.

Learn how to convert trigonometric ratios of non-acute angles, such as sin 197°, cos 245°, and tan 274°, into equivalent trigonometric ratios for acute angles. This problem involves using reference angles, quadrant rules, and the ASTC rule to find correct values.

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