**Trigonometric Function of any Angle**:Consider a right Angle **Triangle ABC** with Angle **∠ C =90°** and side **a, b, c** as shown in the **Figure.**

**Let m ∠ A = θ** Radian

**(1)** the side** AB opposite to 90°** is called **Hypotenuse.**

**(2)** The **side BC opposite to θ** is called the** opposite side,** the side AC

**(3)** The side **AC related To Angle θ** is called **Adjacent side.**

**We can be shown 6 ratios as:**

**a÷b mean a / c**

**b÷c means b / c**

**a÷b means a / b**

**c ÷ a means c/ a**

**c ÷ b means c / b**

**b ÷ a means b / a **

**Why ratio are called trigonometric function:**

In fact, these ratios depend on **only the size** of the Angle and** not on the Triangle formed**. There these ratios are called **trigonometric function** of Angle θ and defined as down.↓

**Trigonometric basic Angle:**

**(1) Sine θ ** : sin θ= a / c = opposite/hypotenuse.

**Reciprocal Angle**

**Cosecant θ** : sin θ= a / c = hypotenuse/opposite

**(2) cosine**** θ ** : cos θ= b / c = Adjacent/hypotenuse.

**Reciprocal Angle**

**Secant θ :** sec θ= c / b =hypotenuse / Adjacent.

**(3) tangent**** θ ** : tan θ= a / b = opposite/ Adjacent.

**Reciprocal Angle**

** cotangent**** θ** : cot θ= b / a =Adjacent/opposite.

**Observation Angle:**

**cosec θ = 1 / sin θ**

**secθ =1/cosθ**

**tanθ =sinθ/ cosθ**

**cotθ= cosθ/ sinθ**

**cot****θ = 1/ tanθ**

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