The hypotenuse of the triangle is the radius of the circle, which is 1. The triangle is placed so that its hypotenuse makes a 30∘ angle with the x-axis, starting from the origin.
To find the coordinates where the triangle (hypotenuse) meets the circle, we use the definitions of sine and cosine for a right triangle:
sinθ=hypotenuseoppositecosθ=hypotenuseadjacent
These are the SOH and CAH formulas.
Since the hypotenuse is 1, the coordinates of the point on the circle at a 30∘ angle from the x-axis are:
Evaluate cos(30∘) and sin(30∘) using a calculator:
cos(30∘)sin(30°)≈0.866(which is actually 2√3)=0.5
So, the intersection point is: