# tangent

1. ### Why this equation is true? Can someone explain?

Can someone explain why this equation is true? I came up with it some time ago and did not understand why it's true: Is there some specific rule for that? Maxima CAS could not tell if it's true, but it is.(Surprised) \frac{2 \tan{\left( \frac{\alpha }{2}\right) }}{\tan{\left( \alpha \right)...
2. ### Hi, I have tried to work out the following...

...can someone help me. Sine cosine tangent angles i have attached the following thanks in advance!
3. ### Internally Tangent Circle Problem Help

Prove: If two circles are tangent internally at point P and the chords PA and (chord) PB of the larger circle intersect the smaller circle at points C and D respectively, then (chord) AB is parallel to (chord) CD.
4. ### Verifying that the tangent is zero (sine function)

Hi, I hope someone can help. I'm currently stuck on a question which requires me to verify that a given function's tangent is zero, by using the difference quotient. As a reminder, the difference quotient follows this form: f(x+h) + f(x)/h. The thing is that I know how to use the difference...
5. ### Inverse Trigonometric Function

if tan x = 1/cot x tan^-1(x) = ?
6. ### Find the equations of the common tangents to parabola and circle

Hi everyone! I'm having some troubles resolving one last point of my weekly sheet.The text says: "Find the equations of the common tangents to the parabola y^2=15*x and the circle x^2+y^2=16." I tried the approach of the discriminant and also one using the distance from a line but both didn't...
7. ### Finding the tangent's gradient at 1!

Hello, I am currently learning about calculus. I have an assignment where I have to find out which point on the curve f(x)=x/x^2+1 the tangent have gradient at 1. I am not sure on how to calculate this, so if anybody can help me, it would be much appreciated :)
8. ### find equation of tangent line to graph at the function given value of x

f(x)= -2x^(1/2)+x^(3/2), x=4. So I know we need a point, and a slope. f(4)= -2(sqrt4) + (sqrt16) with an index of 3. f(4)= -4+ 2(sqrt2) with an index of 3. so are point is (4, -4+ 2(sqrt2) with an index of 3) now we need to find f'(4) to find the slope which is : limit of x approaching...
9. ### find all values of x where tangent line is horizontal

f(x)=2x^3+9x^2-60x+4 this polynomial is not factorable.. do I just put no x values as the answer or what should I put Woops.! My bad. I had to derive this whole equation with the power rule of derivative hehe :D
10. ### tangent of slope

Find the slope of tangent line to curve that is intersection to the surface z= (x^2) - (y^2) with plane x =2 , at point (1,2,3) The ans given by the author is only ∂z / ∂y = -2 Why there's also slope of ∂z/∂x ? Btw, i have sketched out the diagram .....The slope can be both ∂z / ∂y and ∂z/∂x ...
11. ### Hellpppp - The Tangent Function

Hi :) I need some help with graphing tangent functions. a) y = 3tan(x) + √3 Asymptote t = (2k+1)π/2n So t=(2x0+1)π/2x1 = π/2 and -π/2 ~ This answer was correct when I checked the text book x-axis intercepts t = kπ/n t = πx1/1 t=π ~ On the graph in the text book the x axis intercepts were 5π/6...
12. ### Unit tangent vector vs principal normal vector difference

http://mathwiki.ucdavis.edu/Core/Ca.../The_Unit_Tangent_and_the_Unit_Normal_Vectors In the link, I cant understand that why the Principal Unit Normal Vector is defined by N(t) = T'(t) / | T'(t) | ,can someone explain.... Since tangent vector is normal to principal normal vector, why the N(t)...
13. ### Finding the tangent to a circle equation given the circle equation

Hi guys, first time poster here! There' this equation I don't quite understand. I'm given the following question: The tangent line to the curve (x^2) (y^2) − (2x^2) + (y^2) = 0 at the point (1, 1) is=? Not quite sure how to deal with the circle arranged that way? I really need to understand...
14. ### Tangent Line

Okay so I know I need to take the derivative of f(x)=(x^2+12)^(3/4); x=2 but I'm completely lost in this process and don't really know where to begin or how to get the tangent line.
15. ### Eq'n of Tangent Line to y=sinx and...

I have a calc question I haven't been able to crack.
16. ### Points horizontal to tangent plane - Clac 4

Given the surface X2+Y2/9+Z2/9=1 Find the equation of the tangent plane with the points (1/3,2,2) In doing this I found the tangent plane to be Z=-1.5x-y+4.5 The question then asks for you to find a point at which the tangent plane to this surface is horizontal and if there are any such points...
17. ### Finding Equation of a Tangent Line without using Derivatives.

Hey, I'm new. I'm having some trouble. I'm given the problem: y = 4x-3x^2 , (2,-4) I'm unsure about what to do exactly. When do I use the slope of a line formula? When am I supposed to use point slope? When do I utilize the alternative ? Please, and thanks for the help!
18. ### determine the equation of the tangent line at x=1

It is given that e^(xy)=x[(x+1)^3] / (x^2+1) ,where x>0 determine the equation of the tangent line at x=1 my work::::::::xy ln e=lnx+3ln(x+1)-ln(x^2+1) d/dy (xy ln e)=d/dy [(lnx+3ln(x+1)-ln(x^2+1)] dy/dx(1/e)=1/x+[3(1/(x+1))]-[2x/(x^2+1)] dy/dx =e*(1/x+[3(1/(x+1))]-[2x/(x^2+1)]) I know it is...
19. ### finding the equation of a tangent

hi I am trying to find the equation of the tangent to the following curve I have an answer but checking the answer given in text I have seem to have gotten it wrong can anyone help me figure out where I have gone wrong y=\frac{6x-3}{4x+2} at the point 1\frac{1}{2} Right first thing I have to...
20. ### Tangent lines

Hello, Determine the equations of the tangent lines to the graph of f(x)=3x(5x^2+1) that are parallel to the line y=8x+9 This is what I have so far: d/dx(3x(5x^2+1))=45x^2+3 45x^2+3=8 x=-1/3, x=1/3 When I sub this into my formula I get f=-14/9 and f=14/9. does this seem right?