Find the coordinates of the point at the given angle on a circle of radius 3.8 centered at the origin. Given angle is -540 degrees (−540𝑜).

Answer 1

In general, if you have a circle with radius r, and an angle α, then the coordinates of the point on the circle are

(r×cos(α), r×sin(α))

The other general rule you need is that for any α, and any integer k,

sin(α) = sin(α + k×360°)

cos(α) = cos(α + k×360°)

Plugging in your values

(3.8×cos(-540°), 3.8×sin(-540°)) =

(3.8×cos(-540° + 2×360°), 3.8×sin(-540° + 2×360°)) =

(3.8×cos(180°), 3.8×sin(180°)) =

(-3.8, 0)