About Arccot Formula
In trigonometry, the arccot formula is the inverse of the cotangent function, which is defined as the ratio of the adjacent side to the opposite side at a certain angle of a right-angled triangle. Cot-1 is another name for Arccot. The Arccot formula is presented here, along with illustrations.
What is Arccot Formula?
The basic arcot formula will be written as:
θ = arccot(adjacent/opposite)
Examples Using Arccot Formula:
Example 1: In a right-angled triangle DEF, if the base of the triangle is 34 and the height is 22. Find the base angle.
Solution:
To find: θ
Using the arccot formula,
θ = arccot(adjacentopposite)θ = arccot(adjacentopposite)
θ = arccot(3422) = 32.998?θ = arccot(3422) = 32.998?
Answer: Therefore, θ = 32.998?.
Example 2: In a right-angled triangle XYZ, if the base of the triangle is 4 and the height is 3. Find the base angle.
Solution:
To find: θ
Using the arccot formula,
θ = arccot(adjacent/opposite)
θ = arccot(43) = 36.877?
Thus, the value of c is 1.
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Frequently Asked Questions
The Arccot formula, also known as the inverse cotangent function, is defined as:
arccot(x)=tan-1(1/x)
It gives the angle whose cotangent is x, typically measured in radians.
The arccot function can be rewritten using the arctan function as:
arccot(x)=π/2−tan-1(x)
This identity helps in converting between inverse trigonometric functions for more straightforward calculations.
The arccot formula is widely used in geometry, physics, and engineering, especially in solving right-angle triangles, analyzing wave functions, and designing electronic circuits involving phase angles.