Denise is the fastest runner. 40 divided by 6 is 6.666 repeating 30 divided by 5 is 6 and 20 divided by 4 is 5 therefore denise is fastest
Recall that
sin²(<em>x</em>) = (1 - cos(2<em>x</em>))/2
so that
sin²(7<em>π</em>/8) = (1 - cos(7<em>π</em>/4))/2
sin²(5<em>π</em>/8) = (1 - cos(5<em>π</em>/4))/2
Then
sin²(7<em>π</em>/8) + sin²(5<em>π</em>/8) = (1 - cos(7<em>π</em>/4) + 1 - cos(5<em>π</em>/4))/2
… = 1 - 1/2 (cos(7<em>π</em>/4) + cos(5<em>π</em>/4))
… = 1 - 1/2 (1/√2 - 1/√2)
… = 1
