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The tangent (of a curve) is a vector that is tangent (perpendicular to the normal), i.e. the instantaneous velocity of the curve at a specific point. As such, the initial tangent is the initial velocity of the curve at the point where t=0. Stated in other terms, the tangent is the slope of the line at a point. This is expressed (in two dimensions, but applicable to higher dimensions), as the line that has x and y coordinates equal to the point of tangency, and slope equal to the limit of delta y over delta x as delta x (and delta y) approaches zero.
the formula for the arc of a triangle is the arc length is equal to the angle times the radius. s=arc length theta=angle made y length of the arc lenth r=radius s=theta times radius
If y = 2x+1 is a tangent line to the circle 5y^2 +5x^2 = 1 then the point of contact is at (-2/5, 1/5) because it has equal roots
To get the tangent, you first need to find it's slope: y = x2 ∴ dy/dx = 2x So the slope with respect to x is equal to 2x. When x = 2 then, the slope is 4. Now you need the y-coordinate that occurs when x equals 2. We know that y = x2, so when x equals 2, y equals 4. You now have a point on the tangent, as well as it's slope, allowing you to define the line: Recall the definition of a line: Δy = sΔx or: y - y1 = s(x - x1) ∴ y - 4 = 4(x - 2) ∴ y = 4 + 4x - 8 ∴ y = 4x - 4 And that is your tangent.
If the line y = 2x+1.25 is a tangent to the curve y^2 = 10x then it works out that when x = 5/8 then y = 5/2