[Maths Class Notes] on Arctan Formula Pdf for Exam

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.

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