so i have two tangents, and I have to find the point of intersection but i cant get anywhere when i do it
tangents:
y(3cosx)-x(2sinx)=6 and y(3sinx) +x(2cosx)=6
bump
Now that those are cos(theta) etc., all you need to do is find the intersection of two lines. This can be done by solving for x in one of the lines (in terms of y), and plugging this into the other line's equation (i.e. standard procedure of solving two simultaneous linear equations in two unknowns).
Rearranging first tangent equation for x in terms of y:
3ycosA - 2xsinA = 6
2xsinA = 3ycosA - 6
x = 3(ycosA - 2)/2sinA
Sub this into second equation
3ysinA + 2xcosA = 6
3ysinA + 3cosA(ycosA-2)/sinA = 6
3ysin^2 A + 3ycos^2 A - 6cosA = 6sinA
3y (sin^2 A + cos^2 A) = 6(sinA + cosA)
y = 2(sinA+cosA)
Sub y into the first tangent equation
6cosA(sinA+cosA) - 2xsinA = 6
6sinAcosA + 6cos^2 A - 2xsinA = 6
6sinAcosA + 6 - 6sin^2 A - 2xsinA = 6
6sinAcosA - 6sin^2 A = 2xsinA
3cosA - 3sinA = x (sinA doesn't = 0)
x = 3(cosA-sinA)
Therefore they intersect at x = 3(cosA-sinA), y = 2(sinA+cosA)
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