Question

Find the exact length of the curve
b(cos 8 + 20 sin 8), y = b (sin 8 – 20 cosa), 0< theta <π where
b>0.
​

Answer 1

Answer:

We begin by taking the circle of radius 1, centre the origin, in the plane. From the point P on the circle in the first quadrant we can construct a right-angled triangle POQ with O at the origin and Q on the x-axis.

We mark the angle POQ as θ.

Since the length OQ = cos θ is the x-coordinate of P, and PQ = sin θ is the y-coordinate of P, we see that the point P has coordinates

(cos θ, sin θ).

We measure angles anticlockwise from OA and call these positive angles. Angles measured clockwise from OA are called negative angles. For the time being we will concentrate on positive angles between 0° and 360°.