The Hamid family installed a cylindrical pool in their backyard. The
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12. Recall the half-angle identity,
where we take the positive square root because is an angle in a right triangle, which means
, so
. For such an angle, it's always the case that
.
Use the Pythagorean theorem to find the length of the hypotenuse:
Then
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13. is in quadrant II, which means
, so
. In other words,
is in quadrant I, so
. From the half-angle identity we get
###
14. Simplification follows from the definitions of each function:
So we have
###
15. Use the Pythagorean identity:
Then