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lucifer_x
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Homework Statement
If tan^-1 (3/5) = Θ , what is csc^-1 (cotanΘ)
i don't get the question
Csc^-1 is the inverse of the cosecant function. It is also known as the arc-cosecant or inverse cosecant function. The input of this function is the ratio of the length of the hypotenuse to the length of the opposite side in a right triangle. The output is the angle in radians.
CotanΘ is the reciprocal of the tangent function. It is the ratio of the length of the adjacent side to the length of the opposite side in a right triangle. It represents the slope of the line tangent to a point on a circle.
Csc^-1 (cotanΘ) is the inverse of the cotangent of an angle. It can also be interpreted as the angle whose cotangent is the reciprocal of the cosecant. In other words, it is the angle that, when its cotangent is calculated, gives the reciprocal of the cosecant of that angle.
The domain of csc^-1 (cotanΘ) is all real numbers except 0, since the cosecant function is undefined at 0. The range is also all real numbers, as the output of the inverse function can be any angle in radians.
To solve equations involving csc^-1 (cotanΘ), you can use algebraic manipulation and trigonometric identities. It is important to remember that the output of the inverse function is an angle in radians, and to use the appropriate unit when solving the equation. Additionally, it is helpful to use a calculator or a table of values to find the value of the angle.