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 x = Adjacent / Hypotenuse

Cos-1 (Adjacent/Hypotenuse) = x

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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Practise This Question

Variation in gene frequencies within populations can occur by chance rather than by natural selection. This is referred to as :