Given: r = 4/-2-costheta
Is the correct answer -1/2 If not which is the correct answer?
What is the distance between the pole and the directrix?
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4
-4
½
-½
To solve the given equation and find the correct answer, we need to manipulate the equation to put it in a standard form. The given equation is:
r = 4/-2 - cos(theta)
First, we simplify the fraction by dividing both the numerator and denominator by 2:
r = -2 - cos(theta)
Next, we can rewrite the equation in terms of sine instead of cosine. We know that cos(theta) = sin(theta + 90°), so substituting this in the equation, we get:
r = -2 - sin(theta + 90°)
Now, we can rewrite the equation as:
r = -2 - sin(theta)
The equation is now in standard form, where r is the distance from the pole to the point, and theta is the angle the line segment from the pole to the point makes with the positive x-axis.
To find the correct answer, we need to determine the distance between the pole and the directrix. The directrix is a line that is perpendicular to the polar axis and passes through the pole. In this case, the directrix is a horizontal line at a distance of -2 units from the pole on the coordinate plane.
The distance between the pole and the directrix is -2 units. Therefore, the correct answer is -2.