Summary Trigonometry rules-Sine, Cosine and Tangent

### Easy Guide to Sine, Cosine, and Tangent Rules
#### **Introduction to Trigonometry**

Trigonometry is the study relating the angles and sides of right-angled triangles.
The three major trigonometric ratios are **sine (sin)**, **cosine (cos)**, and
**tangent (tan)**.
---

### 1. **Basic Definitions:**

For a right-angled triangle with angle θ:

- **Hypotenuse (H)**: Side opposite the right angle. This is always the longest
side.

- **Opposite (O)**: Side opposite the angle θ.
- **Adjacent (A)**: Side next to the angle θ.
---


### 2. **Sine (sin) Ratio:**

Sine of an angle is the ratio between the **opposite side** and the **hypotenuse**.

- Formula:

sin(θ) = Opposite / Hypotenuse
---

### 3. **Cosine (cos) Ratio:**

Cosine of an angle is the ratio between the **adjacent side** and the
**hypotenuse**.

- Formula:

cos(θ) = Adjacent / Hypotenuse
---

### 4. **Tangent (tan) Ratio:**

The tangent of an angle is defined as the ratio of the **opposite side** to the
**adjacent side**.

- Formula:
tan(θ) = Opposite / Adjacent
---

### 5. **Mnemonic to Remember:**

One nice way to be able to remember the trig ratios is the sentence:

**"SOH CAH TOA"**

- **SOH**: Sine = Opposite / Hypotenuse

- **CAH**: Cosine = Adjacent / Hypotenuse

- **TOA**: Tangent = Opposite / Adjacent