Arctan 1

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In trigonometry, ‘tanθ’ is a trigonometric function where ‘θ’ stands for the angle. The tangent of an angle θ, tanθ is the opposite side divided by the adjacent side in a triangle. Arctan is the inverse of tangent and by taking the inverse tangent, we find the value of θ. Arctan(1) is the inverse tangent of ‘1’ and the angle value of it is 45°.

Example 1: Find the angle, x° if in a triangle the opposite side to angle ‘x’ is 20m and the adjacent side is also 20m.
Given in a triangle, the opposite side = 20m
The adjacent side = 20m

The tangent of an angle, tanx = opposite side/adjacent side
tanx = 20/20
hence tanx = 1
Now in order to find the value of the angle, x we have to get the ‘tan’ to the right side, and it becomes arctan or inverse tangent.
Now we get: x = arctan(1) = 45°
Hence in the triangle, the angle, x = 45°


Example 2: Find the angle, θ° if in a triangle the opposite side to angle ‘θ’ is 60cm and the adjacent side is also 60cm.
Given in a triangle, the opposite side = 60cm
The adjacent side = 60cm

The tangent of an angle, tanθ = opposite side/adjacent side
tanθ = 60/60
hence tanθ = 1
Now in order to find the value of the angle, θ we can take the ‘tan’ to the other side, and it becomes arctan or inverse tangent.
Now we get: θ = arctan(1) = 45°

Hence in the triangle, the angle, θ = 45°
 

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