We are given a diagram that represents a gear with a radius of 10 centimeters. In this diagram, point A represents a 60^(∘) counterclockwise rotation of point P(10,0). Point B represents a θ-degree rotation of point A.
We know the coordinates of B and we want to write these coordinates in terms of cos θ and sin θ.
(10cos ( θ +60^(∘) ), 10sin (θ +60^(∘) ))To do so, we can recall the Angle Sum Identity for cosine.
cos ( A+ B)=cos A cos B - sin A sin B
We will apply this identity to the x-coordinate.
We can follow a similar process to find the y-coordinate. In this case, we can recall the Angle Sum Identity for sine.
sin ( A+ B)=sin A cos B + cos A sin B
Now, we will apply this identity to y-coordinate. Then, we will use the trigonometric values for 60^(∘). Let's do it!
