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 :
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Cos x = Adjacent / Hypotenuse |
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Cos-1 (Adjacent/Hypotenuse) = x |
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Cos-1 (-x) = Π – Cos-1x Cos-1 x = Π – Sin-1 ( \(\begin{array}{l}\sqrt{1-x^{2}}\end{array} \) ) , x<0
Cos-1 x = Sin-1 \(\begin{array}{l}(\sqrt{1-x^{2} }) , x\geq 0\end{array} \)
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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 (Ï€ / 3) = 1 / 2 (Use table of Special Angles)
And also, cos(Π – x) = – cos x.
cos (Ï€ – Ï€/3) = – 1 / 2 …(2)
Compare statement 1 with statement 1
y = Π – Π / 3 = 2 Π /3
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