# Cos Inverse Formula

Cos Inverse is also written as Arccos and Cos-1 and is called an anti trigonometric function. The cos inverse is an inverse trigonometric function with restricted domains.

The Cos inverse Formula is :

 Cos-1 (-x) = Π – Cos-1x Cos-1 x = Π – Sin-1 ($\sqrt{1-x^{2}}$) , x<0 Cos-1 x = Sin-1 $(\sqrt{1-x^{2} }) , x\geq 0$

## Arc cos Questions

Cos inverse formula is one amongst the other six inverse trigonometric functions.

Question: Find the exact Value of Arccos(-½)

Solution:

arccos(- 1 / 2)

Assume y = arccos(- 1 / 2).

cos y = – 1 / 2 with 0 ≤ y ≤ Π (Cos Theorem) … (1)

Cos (π / 3) = 1 / 2 (Use table of Special Angles)

And also, cos(Π – x) = – cos x.

cos (π – π/3) = – 1 / 2 …(2)

Compare statement 1 with statement 1

y = Π – Π / 3 = 2 Π /3

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