standard_description: Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector.
problem_activity: Problem 1
[IMG]
The radius of the circle above is
$$1$$
, and it is centered at the origin. This is called a “unit circle.” Find the coordinates of the point marked at
$${45^{\circ}}$$
.
Problem 2
[IMG]
The radius of the circle above is
$$1$$
, and it is centered at the origin. Find the coordinates of the point marked at
$$150^{\circ}$$
.


aligns: no