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How is an arctangent a crater creator?
In a crater, the slope of the side of the crater is simply the arc-tangent of the height difference divided by the horizontal distance.
What is the function which outputs an angle when a tangent value is input?
The inverse tangent, also called the arc-tangent.
What is the mathematic operation that undoes another mathematic operation?
An inverse operation undoes it's composite operation. For example, Addition and Subtraction are inverses of each other, as are Multiplication and Division, as are Exponentiation and Logarithms, as are Sine and ArcSine, Cosine and ArcCosine, Tangent and ArcTangent, Secant and ArcSecant, Cosecant and ArcCosecant, and Cotangent and ArcCotangent
What is the trigonometric function of -120?
Since you didn't specify which trigonometric function you're using, I'll give you all of them.120 in Degreessin120 ~ 0.87cos120 ~ -0.5tan120 ~ -1.73csc120 ~ 1.15sec120 = -2cot120 ~ -0.58Answer in Degreesarctan120 ~ 89.52arccot120 ~ 0.48120 in Radianssin120 ~ 0.58cos120 ~ 0.81tan120 ~ 0.71csc120 ~ 1.72sec120 ~ 1.23cot120 ~ 1.4Answer in Radiansarctan120 ~ 1.56arccot120 ~ 0.008
Why is the arctangent function restricted to the first and fourth quadrants?
A function cannot be one to many. Suppose y = tan(x) Now, since tan(x) = tan(x + pi) then tan(x + pi) = y But that means arctan(y) can be x or x+pi In order to prevent that sort of indeterminacy, the arctan function must be restricted to an interval of width pi. Any interval of that width would do and it could have been restricted to the first and second quadrants, or even from -pi/4 to 3*pi/4. The problem there is that in the middle of that interval the tan function becomes infinite which means that arctan would have a discontinuity in the middle of its domain. A better option, then, is to restrict it to the first and fourth quarters. Then the asymptotic values occur at the ends of the domain, which leaves the function continuous within the whole of the open interval.
