Question

The value of $y^{\prime} / x^{\prime}$ in terms of the angle 0 is given by
a) $\tan \theta$
b) $\sec \theta$
c) $\cot \theta$
d) $\operatorname{cosec} \theta$

Answer 1

(a)

Explanation:

The value of derivative of a function $f(x)$ is given as $f^{\prime}(x)=y^{\prime} / x^{\prime}$. In terms of theta tangent is the ration of opposite side to adjacent side hence $y^{\prime} / x^{\prime}=\tan \theta$.

Answer 2

The value of \(y^{\prime} / x^{\prime}\) is the derivative of \(y\) with respect to \(x\), often denoted as \(d y / d x\). In the context of trigonometry and polar coordinates, this ratio is often associated with the tangent of an angle.
If you're referring to the angle \(\theta\) (theta), then the ratio \(y^{\prime} / x^{\prime}\) is equivalent to the tangent of the angle \(\theta\), denoted as \(\tan (\theta)\).

This is because in a right triangle, the tangent of an angle is defined as the ratio of the side opposite the angle (often denoted as \(y\) ) to the side adjacent to the angle (often denoted as \(x\) ).
So, \(y^{\prime} / x^{\prime}=\tan (\theta)\)