# tangent

1. ### Help: Tangent parallel to a given plane

Hello; My question is related to finding a tangent plane, which is parallel to a given plane, see the attached picture. I understand the procedure of finding the gradient of the first equation and establishing the normal vector to the surface, then afterwards I get lost. I don't understand...
2. ### How to simplify this expression involving a tangent of 70?

My situation is as follows. Can the expression from below be simplified using precalculus and plain by hand calculation without requiring a calculator? $$B=\sqrt{3} \tan 70^{\circ}- 4 \sin 70^{\circ}+1$$ What I attempted to do was to split the functions in a sum of $30^{\circ}+40^{\circ}$...
3. ### Circle and triangle

A circle k(O) with diameter AB is given. Lines PC and PD touch k (C, D \in k). AC \cap BD = K. Show that PK \bot AB. I have tried to calculate some angles if \angle DCP = \angle PDC = \alpha but it seems useless at the end. I also see that \angle ACB = \angle ADB = \frac...
4. ### Rational Solutions of the tan function in the context of a video game

First of all, I'd like to note that I believe I've already solved the problem I'm about to pose (it just comes down to there being just two rational solutions to the tan function) and as such, am not really in need of help with it. I'm only posting this as a log of a "real-world" application to...
5. ### Exercise on Tangent bundle

Hi everybody, I have to verify that $S'\times S^2$ doesn't have a frame. That's what I would do: $S'$ has a frame so $T_S'= S'\times \mathbb R$. $S^2$ doesn't have a frame so $T_{S^2}\ne S^2 \times \mathbb {R}^2$. $S'\times S^2$ has a frame if and only if \$T_{S'\times S^2}= S'\times S^2 \times...
6. ### equation of a tangent line

Compute an equation of the tangent line to the curve q(s) = (s,sin(Ï€s^2),cos(3Ï€s^2))at the point (2,0,1) where sâˆˆR in this questions my steps will be these: step1: match x,y,z components of the point and q(s) to find parameter s step2: find q'(s) step3: insert parameter...
7. ### Tangent Line

Let me explain my steps for the attached question and please someone confirm me. Compute a unit vector that lies tangent to the curve at the given point. Hint:If you are given a point, you need to first find the t value that produces that point. (a)r(t) =(3...
8. ### Parallel unit vectors

I am at my wits end with this question and hopefully someone can push me in the right direction or offer me some "AH-HA!" advice. Find the unit vectors that are parallel to the tangent line to the curve y = 8 sin(x) at the point (Ï€/6, 4). (Enter your answer as a comma-separated list of...
9. ### Trying to solve the angle of a line tangent on a circle

I've attached the image and I am trying to solve angle "A" of a line that's tangent to a circle. Thanks for your help.
10. ### [ASK] Tangent of a Circle (Again)

If the line x + my = 1 is a tangent of the circle x^2+y^2-4x+6y+8=0, the value of m is .... A. -2 B. \frac{1}{4} C. \frac{1}{4} D. 3 E. 4 Looking at the circle's equation, the center is (2, -3) and the radius is \sqrt5. If I know the coordinate where the line meet the circle I think I...
11. ### [ASK] Tangent of a Circle

One of the tangent line equation of the circle x^2+y^2+6x-8y+12=0 at the point whose abscissa is -1 is .... A. 2x - 3y - 7 = 0 B. 2x - 3y + 7 = 0 C. 2x + 3y - 5 = 0 D. 2x - 3y - 5 = 0 E. 2x - 3y + 5 = 0 By substituting x = -1, I got: (-1)^2+y^2+6(-1)+8y+12=0 1+y^2-6+8y+12=0 y^2+8y+7=0 (y + 1)...

f(x)=ax^2+c dy/dx=2ax Point A (-2,5) lies on the graph of y=f(x). the gradient of the tangent to this graph at A is -6. Find the value of a and c.
13. ### horizontal tangent line

Hi guys, I was wondering how I can solve this question attached. Let me show what I did here but couldn't conclude. Thanks all. f(x) = 2cos(x) + cosÂ²(x) f'(x) = 2sin(x) - 2sin(x)cos(x) => f '(x) = -2sin(x)(1 + cos(x)) and then here sin(x) = 0 OR cos(x) = -1 sin(x) is 0 at pi, 3pi, 5pi...
14. ### Need help calculating coordinates for a tangent point.

So let's say I know coordinates for D (-10171.62, 490.26) angle at that point is 75.52. Also, line EF is a section of a line that starts at -10249, 0 and ends at -10094.8, 7615.2. How do I find the coordinates for A? BTW, the angle at A is 91.16
15. ### Triangle in a circle on a tangent line. Unknown variables.

Thanks for taking the time to help me. I have a geometry, where a triangle lies on a tangent line. I need to be able to define lengths l1, and l2 and angles a3,and a4, using the fixed values in the image. L,a1,a2 are fixed values, along with the center of the circle. When changing the angles...
16. ### Tangent plane to surface

The questions says to find tangent plane to the surface x^2-y^2-3z=0 that goes through A(0,0-1) and is parallel to line : (0,0,0)+t(2,1,2). I'm really stuck here.
17. ### Tangent

Hello :) Can you help me please about the following exercise: There is an elevation f(x, y)=ln(x)+ln(y) when x, y > 0. Show that solving an extreme problem: max{ln(x)+ln(y)} s.t. x+2y=24 sits on point of tangency. The intention is to present only a graphical solution. Thanks a lot!
18. ### tangent lines and chords

Hello everyone, I have a question that I couldn't solve guys. Will you please help me to find x value and explain why? I really appreciate. LEO PS: I read all about tangent lines and chords but couldn't find which theorem is related with this.
19. ### Find the tangent line approximation (#3)

Find the tangent line approximation for f(x) = âˆš(15 + x) near 0
20. ### Find the tangent line approximation

Find the tangent line approximation for f(x) = 1/x near x=8 so I used the f(a) +f'(a)(x-a) f = 1/x f' = -1/x^2 I end up writing y - 1/8 = -1/64 (x + 8) my answer I get is -1/64 - 1/4, but it's wrong so I am stuck. :/ Any help?