You are watching: Arctan(-1/2)
By restricting domain that the principal tangent function, we achieve the station tangent that arrays from −π/2 to π/2 radians exclusively. However, the domain of one arctangent duty is all real numbers. The graph climate looks as follows:
How is this arctan graph created? By showing the tan(x) in the (-π/2 π/2) selection through the line y = x. Girlfriend can likewise look in ~ it together swapping the horizontal and vertical axes:
Arctan properties, relationships v trigonometric functions, integral and derivative of arctan
The relationships in trigonometry are critical to expertise this subject even more thoroughly. Inspecting the right-angled triangle through side lengths 1 and x is a an excellent starting point if you want to find the relationships in between arctan and the simple trigonometric functions:Tangent: tan(arctan(x)) = x
Other advantageous relationships through arctangent are:arctan(x) = π/2 - arccot(x)arctan(-x) = -arctan(x)integral of arctan: ∫arctan(x) dx = x arctan(x) - (1/2) ln(1 + x²) + Carctan(x) + arctan(1/x) = π/2, because that x > 0 and also arctan(x) + arctan(1/x) = -π/2, for x
It's simple to prove the first equation from the nature of the ideal triangle v side lengths 1 and x, as we perfectly know that the sum of angles in a triangle equates to 180°.
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Subtracting the appropriate angle, i m sorry is 90°, we're left with two non-right angles, which have to sum as much as 90°. Thus, we deserve to write the angle as arctan(x) and also arctan(1/x).