ARCTANGENT

Arctangent

Definition Of Arctangent

Arctangent is the inverse function of tangent. It is also written as arctan or tan^-1. If y = tan x, then x = arctan y.

Examples of Arctangent

tan^-1 1 = 45⁰ or arctangent (1) = 45⁰. This means that the angle 45⁰ has tangent equal to 1.

Video Examples: Arctan Inverse Trig Function

Solved Example on Arctangent

Ques: Find the value of sec [arctan ].

Choices:

A.
B.
C.
D.
Correct Answer: B

Solution:

Step 1: Let B = arctan . Then tan B = .
Step 2: So, sec [arctan ] = sec [arctan(tan B)].
Step 3: = sec B
Step 4: From the figure, we observe that sec B = .
example of Arctangent Step 5: So, sec[arctan ] = .

Quick Summary

Arctangent is the inverse of the tangent function.
It's denoted as arctan(x) or tan⁻¹(x).
It gives the angle whose tangent is x.
The range of arctangent is (-π/2, π/2) radians or (-90°, 90°).

\[ x = \arctan(y) \Leftrightarrow y = \tan(x) \]

🍎 Teacher Insights

Emphasize the difference between arctangent and the reciprocal of tangent. Use the unit circle to visually represent the relationship between tangent and arctangent. Provide real-world examples where arctangent is used, such as finding the angle of elevation.

🎓 Prerequisites

Tangent function
Inverse functions
Unit circle
Pythagorean theorem

Check Your Knowledge

Q1: What is arctan(1)?

0 π/4 π/2 π

Q2: The range of arctangent function is?

(0, π) [0, π] (-π/2, π/2) [-π/2, π/2]

Frequently Asked Questions

Q: What is the domain of the arctangent function?
A: The domain of the arctangent function is all real numbers.

Q: What is the range of the arctangent function?
A: The range of the arctangent function is (-π/2, π/2) radians or (-90°, 90°).

Q: How do I find the arctangent of a number?
A: Use a calculator or trigonometric tables to find the angle whose tangent is the given number.