Inverse circular functions:

If sinθ = x, then q any angle whose sine is x, and we can write θ= sin^-1x. It means that q is an angle which is determined from its sine. Therefore tan^-1 1/√3 is an angle the tangent of which is 1/√3, i.e. q = tan^-11/√3= nΠ + Π/6 here Π/6 is least positive value of q.

The functions sin^-1 x, cos^-1 x, tan^-1 x, cot^-1 x, sec^-1 x and cosec^-1 x are called as inverse circular or inverse trigonometric functions.

If x is positive, principal values of all inverse circular functions lie between 0 and Π/2. If x is negative, principal values of sin^-1 x, cosec^-1 x and tan^-1 x lie between Π/2 and 0, and those of cos^-1 x, sec^-1 x and cot^-1 x lie between Π/2 and Π From now onwards we take only principal values.

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