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 img].

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


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