- #1
Maxwellkid
- 69
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How do u tak the derivative of
X = (cos@)/(sin@)
dx/d@ = ?
X = (cos@)/(sin@)
dx/d@ = ?
Maxwellkid said:must I merely memorize the derivate of cotangent?
To simplify this expression, we can use the trigonometric identity tan@ = sin@/cos@. This means that X = cos@ * (1/sin@) = cot@, which is the cotangent of @.
The domain of this expression is all real numbers except for values of @ that make sin@ equal to 0, since division by 0 is undefined. In other words, the domain is all real numbers except for values of @ that are integer multiples of π.
The range of this expression is all real numbers, since the cosine and sine functions have a range of [-1, 1] and we are dividing by sin@ which can take on any value except 0. Therefore, the range of X is (-∞, ∞).
The graph of this expression is the graph of the cotangent function. It has vertical asymptotes at integer multiples of π and a period of π. It also has a range of (-∞, ∞) and a domain of all real numbers except for the vertical asymptotes.
This expression is commonly used in various fields of science, such as physics and engineering, for calculating the relationship between two variables in a right triangle. The ratio of the adjacent side (cos@) to the opposite side (sin@) is equal to the cotangent of the angle (@) between them. This is useful for solving problems involving forces, velocities, and other quantities involved in the study of motion and mechanics.