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:
arctan(x) = 2arctan (x/1+√1+x2)
arctan(x) = ∫x0 1/z2+1dz;|x|≤1
∫arctan(z) dz = z arctan(z) – 1/2 ln(1+z2) + C
Arctangent formulas for π are as given below:
π/4 = 4 arctan(1/5) - arctan(1/239)
π/4 = arctan(1/2) + arctan(1/3)
π/4 = 2 arctan(1/2) - arctan(1/7)
π/4 = 2 arctan(1/3) + arctan(1/7)
π/4 = 8 arctan(1/10) - 4 arctan(1/515) - arctan(1/239)
π/4 = 3 arctan(1/4) + arctan(1/20) + arctan(1/1985)
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.
In the right-angled triangle PQR, the base of which measures 17 cm and the height is 9cm. Determine the base angle.
To calculate: base angle
How: Using arctan formula
θ = arctan(opposite ÷ adjacent)
θ = arctan(9 ÷ 17)
θ = 27.47 degrees or 270
Answer: The angle is 270
Find out the value of θ, given that the base of the triangle ABC is 24 ft and the height is 11 ft
arctanθ = opposite / adjacent
arctanθ = 11 ÷ 24 =0.24
arctanθ = 24.60
θ = 240