Answer:
(a) This expression would be more easily represented by a Cartesian equation, since distance with respect to origin varies with angle. ([tex]r = f(\theta)[/tex]). The line is represented by [tex]y = 0.577\cdot x[/tex].
(b) This expression would be more easily represented by a Cartesian equation, since distance with respect to origin varies with angle. ([tex]r = f(\theta)[/tex]). The resulting equation is [tex]x = 5[/tex].
Step-by-step explanation:
(a) This expression would be more easily represented by a Cartesian equation, since distance with respect to origin varies with angle. ([tex]r = f(\theta)[/tex]) A straight line is represented by the following expression:
[tex]y = m\cdot x + b[/tex]
Where:
[tex]x[/tex] - Independent variable, dimensionless.
[tex]y[/tex] - Dependent variable, dimensionless.
[tex]m[/tex] - Slope, dimensionless.
[tex]b[/tex] - y-Intercept.
From Analytical Geometry we know that slope is equal to:
[tex]m = \tan \theta[/tex]
Where [tex]\theta[/tex] is the angle of the line with respect to the positive x-axis, measured in radians.
If we know that [tex]\theta = \frac{\pi}{6}\,rad[/tex], then:
[tex]m = \tan \frac{\pi}{6}[/tex]
[tex]m \approx 0.577[/tex]
The y-intercept is found by replacing independent and dependent variables by known point:
[tex]0 = 0.577\cdot (0) + b[/tex]
[tex]b = 0[/tex]
Therefore, the line is represented by [tex]y = 0.577\cdot x[/tex].
(b) This expression would be more easily represented by a Cartesian equation, since distance with respect to origin varies with angle. ([tex]r = f(\theta)[/tex]) A straight vertical line is represented by:
[tex]x = a[/tex]
Since slope becomes indefined by applying the definition used in (a).
Since that line passes through (5, 5), the value of [tex]a[/tex] is 5. Then, the resulting equation is [tex]x = 5[/tex].
