AboutSteve Holleran Expertise I can help with all math questions from basic math to Calculus.
Whether it`s consumer questions, or questions from high school or college students, I have probably dealt with it at some time in my career.
Experience 33 years teaching experience in NJ public schools
Education/Credentials B.S. Mathematics : Wake Forest University 1972
M.S. Mathematics : Monmouth University 1981
Expert: Steve Holleran Date: 5/10/2008 Subject: Trigonometry
Question If sinx=3cosx, what is the value of sinxcosx?
I tried subbing it in but can't seem to get the answer.
Answer Hi Patrick,
I came up with something by trying this:
sin x = 3 cos x ------------> sin x / cos x = 3
so tan x = 3 = 3/1. Now , if you diagram a first quadrant right triangle, tangent = opposite / adjacent, so the opposite (vertical) side would be 3, the adjacent (horizontal) side would be 1, and that would make the hypotenuse sqrt(10).
Then you would have
sin x = opp/hyp = 3/sqrt(10),
cos x = adj/hyp = 1/sqrt(10)
so that sin x cos x = 3/sqrt(10) * 1/sqrt(10) = 3/10.
