1.Prove the following identity, assuming that A, B, and C are the three angles of some triangle ABC
cos(C) = (sin(A))(sin(B))-(cos(A))(cos(B))
2. A rectangular tunnel is cut through a mountain to make a road. The upper verticies of the rectangle are on the circle x^2+y^2=400.
Show that the cross-sectional area of the end of the tunnel is 400sin(2theta).
It says "Hint: Write the coordinates of the point in the upper right vertex of the rectangle in terms of sine and cosine"
But I don't know what they are
3. Find the dimensions of the rectangular end of the tunnel that maximizes its cross-sectional area.
the formula x^2+y^2=400 on top of the circle, and (x,y) next to a line leading up to what I assume is the upper right vertex
cos(C) = (sin(A))(sin(B))-(cos(A))(cos(B))
2. A rectangular tunnel is cut through a mountain to make a road. The upper verticies of the rectangle are on the circle x^2+y^2=400.
Show that the cross-sectional area of the end of the tunnel is 400sin(2theta).
It says "Hint: Write the coordinates of the point in the upper right vertex of the rectangle in terms of sine and cosine"
But I don't know what they are
3. Find the dimensions of the rectangular end of the tunnel that maximizes its cross-sectional area.
the formula x^2+y^2=400 on top of the circle, and (x,y) next to a line leading up to what I assume is the upper right vertex