how are the 30 degree, 45 degree, and the 60 degree coordinates on the unit circle are derived/

Question

I need help with problems related to the unit circle

Answer 1

 

Hi Heer,

 

For a point on the circle of which radius is r and

angle measured counterclock-wise from the x-axis is θ,

its x-coordinate and y-coordinate are given by r·cosθ and r·sinθ, respectively.

 

For the special case of the unit circle,

its x-coordinate and y-coordinate are given by cosθ and sinθ, respectively.

 

When θ = 30°, (x, y) = (cos(30°), sin(30°)) = (√3/2, 1/2).

 

When θ = 45°, (x, y) = (cos(45°), sin(45°)) = (√2/2, √2/2).

 

When θ = 60°, (x, y) = (cos(60°), sin(60°)) = (1/2, √3/2).