area of a triangle = (1/2)(base)(height) ... the rectangle is made up of 4 congruent triangles.
Don't forget the double angle identity for sine ... you'll need it.
I am not good with these certain types of problems. It has 3 parts to the question:
A) Verify that A(theta)=25sin2(theta) models the area of the rectangle. Justify your verification and determine the domain for theta.
B) Use your calc. to find the largest possible area for such a rectangle.
C) What are the dimensions of the inscribed rectangle with the largest possible area?
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This is what i got: (t = theta)
25sin(2t) = 25(2sin(t)cos(t)) = 50sin(t)cos(t)
area of rectangle: (4)(1/2)(5cos(t))(5sin(t)) = 2(25cos(t)sin(t)) = 50sin(t)cos(t).
Is this correct?
NOTE: ALSO ON THE PAPER IT SAYS THE SEMI CIRCLE HAS A RADIUS OF 5cm. Forgot to add that in the beginning.