Tagged Questions
3
votes
2answers
57 views
Why do we need to find the intersection between these lines?
We have the functions
$$ x = -1 + 2 \cos(t)$$
$$ y = 3 + 2 \sin(t)$$
They give P's orbit
with $t$ on $\left[0, \dfrac{3}{2} \pi\right]$
Find (to 2 decimal places accurate) for which values of t ...
0
votes
0answers
47 views
Torus equation in terms of tangent
So if I have an equation for a torus in $F(a,b) = (X, Y, Z)$ where $X = (R + r\cos a)\cos b$ and $0 < r < R$, how would I go about rewriting this equation for $X$ in terms of $\tan(a/2)$ and ...
3
votes
1answer
152 views
How are the parametric equations describing the cupid curve derived? [duplicate]
No doubt as some people have already seen, today morning wolfram posted the best valentine ever. The graph depicting cupid with its arrow and floating hearts around it involves something like 6 pages ...
2
votes
2answers
55 views
Converting $x = \sin \frac{t}{2}, y = \cos \frac{t}{2}$ to Cartesian form
How can we transform these parametric equations to Cartesian form?
$$x = \sin \frac{t}{2}, \quad y = \cos \frac{t}{2}, \quad -\pi \leq t \leq \pi.$$
0
votes
1answer
118 views
Arc Length Of Parametric Curve
I attached the problem as a file:
Where did the trig functions go? I sifted through the different trig identities and formulas, but couldn't find anything that I could use. What should I do?
1
vote
1answer
63 views
Restriction Of Parametric Functions Domain
The problem I am working on is, "Sketch the curve represented by the parametric equations (indicate the orientation of the curve), and write the corresponding rectangular equation by
eliminating the ...
1
vote
1answer
214 views
Parameterize a straight line using polar coordinates… without angle.
I had to parameterize a straight line with starting point in $A=(-3,7)\\ $ and endpoint in $B=(4,1)$.
My idea was to use the equation for the line that goes through two points. That is:
$$
\frac { ...
28
votes
3answers
1k views
Do “Parabolic Trigonometric Functions” exist?
The parametric equation
$$\begin{align*}
x(t) &= \cos t\\
y(t) &= \sin t
\end{align*}$$
traces the unit circle centered at the origin ($x^2+y^2=1$). Similarly,
$$\begin{align*}
x(t) ...
1
vote
1answer
217 views
2
votes
1answer
106 views
Finding Angle of Elevation to hit X, Y
My ultimate goal is to find the angle of elevation necessary to launch a projectile from the origin to (x,y) with initial velocity V and under gravitational acceleration g. Wind resistance is ignored.
...
