Asked by meet
If A+B=90° then what is the range of SinA•SinB
Answers
Answered by
Reiny
since A+B = 90
B = 90-A
and sinB = sin(90-A) = cosA
similarly cosB = sinA
sinAsinB = sinAcosA = (1/2)sin 2A
thus y = (1/2)sin 2A
has an amplitude of 1/2
so the range is -1/2 ≤ y ≤ 1/2
B = 90-A
and sinB = sin(90-A) = cosA
similarly cosB = sinA
sinAsinB = sinAcosA = (1/2)sin 2A
thus y = (1/2)sin 2A
has an amplitude of 1/2
so the range is -1/2 ≤ y ≤ 1/2
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