In trigonometry mathematics, every function has an inverse and arctan is the inverse of the tangent function. Arctan is also referred to as the tan-1. Arctan x is used to find the angle. The tangent on the other hand is described as the ratio of the opposite side to the adjacent side of a particular angle of a right-angled triangle. Arctan formula is used to identify an angle.
What is the Arctan Formula?
A fundamental arctan formula is written as:
Other arctan formulas are as given below:
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arctan(x) = 2arctan (x/1+√1+x2)
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arctan(x) = ∫x0 1/z2+1dz;|x|≤1
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∫arctan(z) dz = z arctan(z) – 1/2 ln(1+z2) + C
Arctangent formulas for π are as given below:
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π/4 = 4 arctan(1/5) – arctan(1/239)
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π/4 = arctan(1/2) + arctan(1/3)
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π/4 = 2 arctan(1/2) – arctan(1/7)
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π/4 = 2 arctan(1/3) + arctan(1/7)
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π/4 = 8 arctan(1/10) – 4 arctan(1/515) – arctan(1/239)
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π/4 = 3 arctan(1/4) + arctan(1/20) + arctan(1/1985)
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π/4 = 24 arctan(1/8) + 8 arctan(1/57) + 4 arctan(1/239)
Solved Examples Using Arctan Formula
The arctan formula can be thoroughly understood for use and application referring to solved examples below.
Example:
In the right-angled triangle PQR, the base of which measures 17 cm and the height is 9cm. Determine the base angle.
Solution:
To calculate: base angle
How: Using arctan formula
θ = arctan(opposite ÷ adjacent)
θ = arctan(9 ÷ 17)
= arctan(0.52)
θ = 27.47 degrees or 270
Answer: The angle is 270
Example:
Find out the value of θ, given that the base of the triangle ABC is 24 ft and the height is 11 ft
Solution:
arctanθ = opposite / adjacent
arctanθ = 11 ÷ 24 =0.24
arctanθ = 24.60
θ = 240