Question

2. Find the angle of intersection between the curves r?sin20 = 4 and r2 = 16 Sin20.​

Answer 1

Answer:

r² = 16sin20 is 19.754 degrees or 0.348 radians.

Explanation:

From the above question,

They have given :

The second curve is given by: r^2 = 16 * sin(20)

To find the point(s) of intersection, we can set the two equations equal to each other:

 r * sin(20) = $r^2$ / 16 * sin(20)

This simplifies to:

               r = 4

So the point of intersection is (4, 20) in polar coordinates.

Next, we need to find the angle of intersection between the two curves at this point.

We can use the property that the angle between two curves at a point of intersection is given by the difference between the angles of the tangents to the two curves at that point.

The angle of the tangent to the first curve at the point of intersection is 20 degrees (since it is the polar angle of the point).

The angle of the tangent to the second curve at the point of intersection can be found by differentiating the equation of the curve with respect to r. The derivative of the equation is:

$r = (16sin(20))^(1/2)$

So, the angle of the tangent to the second curve is arctan((dr/d(theta))/(1)) = arctan(1/4) = 14.04 radians or 0.246 radians

Finally, the angle of intersection between the two curves is:

                 = 20 - 0.246

                = 19.754 degrees or 0.348 radians

So, the angle of intersection between the curves,

     r*sin20 = 4 and

              r² = 16sin20 is 19.754 degrees or 0.348 radians.

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