tangent

1. Secant and Tangent Question

Hi, I need help with this problem. It is in the attachment. Am I supposed to use the formula y2-y1/x2-x1 for this problem?
2. Simplify trigonometric function in terms of tangent

Simplify (4 \cos^2 9^\circ -3)(4\cos^2 27^\circ -3 ) in terms of tangent.
3. How to move point 'p' through a tangent.

If I have point p defined as P(x,y) where : Sin(theta) = y/r and Cos(theta) = x/r. How can I move point p through a tangent so that 'P' is then twice the distance from the origin ?
4. the point tangent to line

At what point on the curve xy = ( 1 - x - y)^2 is the tangent line parallel to the x - axis need your assistance here guys...
5. identify tangent line

there are two lines AB and CD which one is tangent line and why? I know they say AB is tangent line but how to Mathematically( Geometrically(Trigonometrically )) prove it? we can take tangent theta too and tangent psi too then both are through tangent of some angle so aren't they both tangent...
6. Regarding a Line Tangent to a Circle

Hello Math Help Forum, I'm new here, and would first of all like to say hi :) I am currently working on a 2D Lighting Engine software, and need to be able to determine a certain point (or at least the equation of the line passing through it). Here's an illustration: What I would like to do...
7. Siplification Needed For Tangent Slope

Find an equation of the tangent line to the curve at the given point: y=(x-1)/(x-2), (3,2) And I am using the the formula: lim as x approaches a = [f(x) - f(a)]/(x-a). So plugging in what we already know, we get: [x-1/x-2 - 2]/x-3 = slope of the tangent line Sooooo I'm wasn't sure how to...
8. Find the equation of a tangent

I need to find the equation of the tangent to the curve xy2 + 3x -2y=6. at the point (2,1) I know I need to differentiate implicitly but its getting confusing differentiating the xy2 After differentiation then id set the function dy/dx to equal 0?
9. Tangent plane to a surface

Hello all, I am studying for a calc three test and came across a problem I got stuck on the problem is as follows. given the function g(x,y,z)= x^2 ln y+y z find an equation for the tangent plane to the surface g(x,y,z) =2 at the point (2,1,2) I started of by finding the gradient of g(x,y,z)...
10. Tangent to a curve

Consider the function f(x)= x^2+k, k\in \mathbb{R} and the tangent to the curve at x=a Show that the tangent does not pass through the origin if k<0 . It seems obvious that it does that it pass through the origin when I draw the function for k<0 as the origin is 'inside' the parabola. But is...
11. Tangent from a point to a curve?

I have an important exam on Monday and I stumbled upon this problem. Problem: Calculate the angle (with tan(x) function) between the tangent lines drawn from (-4,1) point to a graph y^2=2*x. I know that derivative of function represents its tangent line equation, however I cannot seem to...
12. Finding the eq. of tangent line to this curve..

Hi! I'm struggling with this problem Find an equation of the tangent line to the curve at the point (1, 8). I am stuck because while I'm solving this, I keep getting 0/0. How would you solve this problem? Thanks!
13. Equation of the tangent to a perpendicular lin

Can someone help me to solve this : Find the equation of the tangent to the curve x2 -2xy + 2y2 -7x + 6y + 6 = 0 which is perpendicular to 6x + 5y -4 = 0
14. Unit tangent vector

I am trying to find the unit tangent vector T(t) Heres the problem r(t) = ti + \frac{1}{t}j, t = 1 v(t) = i - \frac {1}{t^2} j then a(t) = \frac {2}{t^3} j I think the magnitude is: ||v(t)|| = \sqrt \frac{2} {t^4} j then the solutions manual has this: T(t) = \frac {v(t)}{ ||...
15. slope of tangent line

(a) Find the slope of the tangent line to the curve y = 9-x2 at the point whose x-coordinate is 2. (b) Find the equation of this tangent line in a slope-intercept form.
16. Are there identities for inverse tangent?

Are there identities for inverse tangent? Can you verify them [the identities] for me? I know two of them: arctan(x)=arccot(1/x) arctan(x)=pi/2-arccot(x) What is the third one if the identity exist? And Why? Thank you in advance.
17. Why's that normal = binormal x tangent for a curve parametrized by arc length s?

I'm stuck at the properties of a 3d curve parametrized by arc length. My problem is given below. We know that the binormal of a curve at a point is: b = n \times t where b = binormal and n is normal to the curve and t is tangent. So binormal is the cross product of normal and tangent at a...
18. Integration of tangent hyperbolic function containing a function of x

Hi please any one can help me in solving the attached integral? Thank you
19. Find the equation of the tangent plane to the surface (vector calculus)

Find the equation of the tangent plane to the surface z=x(x^2+y)^1/2 at the point (2,5,6) thank you
20. Writing the equation of a tangent line

I'm reviewing for the AP exam and would love it if someone could walk me through this problem- I know you find the derivative of the curve at the given point... but I get lost from there The slope of a function f at any point (x,y) is y/(2x)^2. The point (2,1) is on the graph of f. A. Write an...