# Please explain the meaning of sin^-1, cos^-1, tan^-1 in terms of sin, cos,tan respectively

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Let us take a right angle triangle ABC, with right angle at B.

Sine of A is defined as BC / AC = opposite side to angle A / hypotenuse

example: Sin 30 deg = 1/2

We want to know the value of angle A, but we may not directly know it. Then we can calculate its sine value from other quantities in some way, and then find its value as:

Thus we define as equal to angle A.

Same way, we know

so we define

Similarly we know the tangent

We want to find the angle C, when we are given AB and BC. So we define a function

So sine cosine, tangent of angles give ratio of sides in a right angle triangle. The inverse functions give the values of angles from ratio of sides.

Sine of A is defined as BC / AC = opposite side to angle A / hypotenuse

example: Sin 30 deg = 1/2

We want to know the value of angle A, but we may not directly know it. Then we can calculate its sine value from other quantities in some way, and then find its value as:

Thus we define as equal to angle A.

Same way, we know

so we define

Similarly we know the tangent

We want to find the angle C, when we are given AB and BC. So we define a function

So sine cosine, tangent of angles give ratio of sides in a right angle triangle. The inverse functions give the values of angles from ratio of sides.