Question

Cheyenne has a pizza. The radius of a pizza is 4 inches, and the pizza is cut into 8 slices. How many radians of the pizza are taken if two slices were eaten? What is the degree measure of the two slices taken? Explain your steps.

Answer 1

we know that

a full circle is a 360 degrees or 2*pi radians
the pizza is cut into 8 slices
so
360°/8-----> 45° each slice
2*pi/8-----> 0.785 radians each slice

part 1) How many radians of the pizza are taken if two slices were eaten?
2*0.785=1.57 radians

the answer Part 1) is
1.57 radians

Part 2) What is the degree measure of the two slices taken?
2*45°=90°

the answer Part 2) is 90°

Part 3)
simplify the following
[cos²∅*tan²∅]/[1-sin²∅]------> equation 1

we know that
sin²∅+cos²∅=1
cos²∅=1-sin²∅-----> equation 2

substitute equation 2 in equation 1
[cos²∅*tan²∅]/[1-sin²∅]------> [cos²∅*tan²∅]/[cos²∅]----> tan²∅

the answer Part 3) is
tan²∅