Question

A circle centered at the origin has a radius of 10 units. The terminal side of an angle, Theta, intercepts the circle in Quadrant I I at point C. The y-coordinate of point C is 8. What is the value of cosine theta?

Answer 1

Since the circle is centered at the origin, we can use the equations
x² + y² = r²
x = r cos θ
y = r sin θ

We know y = 8 and r = 10. Solving for x
x² + 8² = 10²
x = 6

From this equation:
x = r cos θ
6 = 10 cos θ
cos θ = 6/10 = 0.6