Unfortunately, the browser used for posting questions is hopelessly inadequate for mathematics: it strips away most symbols. All that we can see is "tangent line Yex(1-cosx) xpi2". From that it is not at all clear what the missing symbols (operators) might be. It makes little sense for me to try and guess - I may as well make up my own questions and answer them!
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To measure the point at which two tangents intersect each other, find an equation for each tangent line and compute the intersection. The tangent is the slope of a curve at a point. Knowing that slope and the coordinates of that point, you can determine the equation of the tangent line using one of the forms of a line such as point-slope, point-point, point-intercept, etc. Do the same for the other tangent. Solve the two equations as a system of two equations in two unknowns and you will have the point of intersection.
a tangent is a line that touches the circle at only ONE point
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According to Wikipedia.'Suppose that a curve is given as the graph of a function, y = f(x). To find the tangent line at the point p = (a, f(a)), consider another nearby point q = (a + h, f(a + h)) on the curve. The slope of the secant passing through p and q is equal to the difference quotientAs the point q approaches p, which corresponds to making h smaller and smaller, the difference quotient should approach a certain limiting value k, which is the slope of the tangent line at the point p. If k is known, the equation of the tangent line can be found in the point-slope form:'
Suppose a curve is defined by the function y = f(x) and you want the equation of the tangent at the point A.Suppose the x-coordinate at A is p. Then use y = f(p) to find the y-coordinate of A and let that be q. So, the point A is (p, q).Next, find dy/dx, the derivative of the function f, with respect to q. This will be a constant or a functio of x. In the latter case, find its value for x = p. This is m, the gradient of the tangent.So now you have the tangent line with gradient, m which passes through the point (p, q) and so its equation isy - q = m(x - p)Simplify this into the required form: y = mx + c or ax + by + c = 0.