ok so i used tan[theta] = y/x to get y =xtan[theta] for the equation of the line. i think it worked out. does that make sense tho? does that form a radial line originating from the center.
ok so here's the question
A lighthouse is located 9 miles south of the center from the center of a circular island of diameter 10 miles in d.When the beam is over the island the beam enters at a point on the shore and leaves at another point,. As the beam rotates the distance between these...
in the question however it states that the beam passes through the circle as function of theta. so can i say this in addition to wat you wrote.
In[1]:= Reduce[{y==(7x/3)Tan[θ],x^2+(y-9)^2==5^2},{x, y}, Backsubstitution->True]
would this now solve for the intersection as a function of theta?
Given an equation for a line y=7x/3, how can i define it in mathematica using x,y and theta.
I am eventually going to have to find the intersection of this line to a circle with the equation Circle[{0,9},5] as a function of theta.
I thought maybe if i use the rule tan(θ) = y/x then id get...