Find the point x y on a circle of radius 7 centered at the o

Find the point (x, y) on a circle of radius 7 centered at the origin that corresponds to the standard position angle theta = 5 pi/3 radians. Give exact and decimal answers. Give two real-world examples of phenomena that are periodic, i.e., that exhibit repetitive behavior - besides spinning wheels and clocks. The radius of Planet Earth is 3960 miles. Find the number of miles spanned by one degree of latitude.

Solution

a. R=7   theta= 5pi/3 radians

x= R cos theta       y= R sin theta

x=7 cos (5pi/3)         y= 7sin (5pi/3)

x=7/2                       y= -7sqrt3/2

In exact form point is (7/2,-7sqrt3/2)

In decimal form point is (3.5, 6.06)

4. Radius,r= 3960 miles

   theta= 1 degree= pi/180 radian

arc length ,s= r * theta = 3960 *pi/180 =   69.08 miles