Trigonometric Function of any Angle

Trigonometric Function of any Angle

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.

Trigonometric Function of any Angle

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

cotθ = 1/ tanθ