How to find the general and principal values of cot\(^{-1}\) x?
Let cot θ = x (- ∞ < x < ∞) then θ = cot\(^{-1}\) x.
Here θ has infinitely many values.
Let – \(\frac{π}{2}\) ≤ α ≤ \(\frac{π}{2}\), where α is positive or negative smallest numerical value of these infinite number of values and satisfies the equation cot θ = x then the angle α is called the principal value of cot\(^{-1}\) x.
Again, if the principal value of cot\(^{-1}\) x is α (α ≠ 0, – π/2 ≤ α ≤ π/2) then its general value = nπ + α.
Therefore, cot\(^{-1}\) x = nπ + α, where, (α ≠ 0, – π/2 ≤ α ≤ π/2) and ( - ∞ < x < ∞ ).
Examples to find the general and principal
values of arc cot x:
1. Find the General and Principal Values of cot\(^{-1}\) √3
Solution:
Let x = cot\(^{-1}\) √3
⇒ cot x = √3
⇒ cot x = tan (π/6)
⇒ x = π/6
⇒ cot\(^{-1}\) √3 = π/6
Therefore, principal value of cot\(^{-1}\) √3 is π/6 and its general value = nπ + π/6.
2. Find the General and Principal Values of cot\(^{-1}\) (- √3)
Solution:
Let x = cot\(^{-1}\) (-√3)
⇒ cot x = -√3
⇒ cot x = cot (-π/6)
⇒ x = -π/6
⇒ cot\(^{-1}\) (-√3) = -π/6
Therefore, principal value of cot\(^{-1}\) (-√3) is -π/6 and its general value = nπ - π/6.
● Inverse Trigonometric Functions
11 and 12 Grade Math
From General and Principal Values of arc cot x to HOME PAGE
Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.
Mar 02, 24 05:31 PM
Mar 02, 24 04:36 PM
Mar 02, 24 03:32 PM
Mar 01, 24 01:42 PM
Feb 29, 24 05:12 PM
New! Comments
Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.