Consider a circle with radius 4 that is centered at the origin. Find the exact x and y coordinates of the point on this circle corresponding to an angle -1𝝅/3

Question

x = __________

y = __________

Answer 1

In order to answer this, we need to remember the trig values of benchmark angles (π/6 , π/4 , and π/3 in all 4 Quadrants), and we need to remember the coordinate plane definitions of sine and cosine for a circle of radius r instead of 1.

For our circle of radius 4, the coordinates of the point of intersection with Θ's terminal ray are (4cosΘ , 4sinΘ).

Since Θ = - π/3 , x = 2 and y = - 2√3.