# Tagged Questions

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### Trigonometric Partial Derivative

I need to find $$\frac{\partial Z}{\partial U} \text{ and } \frac{\partial Z}{\partial V}$$ for a $z=f(x,y) = \cos(xy) + y\cos(x)$. After a bit of an internet search, I think I have found the ...
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### Parametric Equation of sine wave helically wrapped around a cylinder

I want a parametric equation of a sine wave at a small ramp angle wrapped around a cylindrical body (3D). The parametric equation below gets me close to what I'm looking for, but not quite since the ...
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### Convolution integral $\int_0^t \cos(t-s)\sin(s)\ ds$

How can I calculate the following integral? $$\int_0^t \cos(t-s)\sin(s)\ ds$$ I can't get the integral by any substitutions, maybe it is easy but I can't get it.
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### A Hard integral in 2-D.

I'm having a trouble integrating (in $\mathbb{R}^2$) the following formula: $$\frac{t}{|B(x,t)|}\int_{B(x,t)} \frac{||y||}{(t-||x-y||^2)^{\frac{1}{2}}} dy$$ where $B(x,t)$ is the ball with center ...
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### Directional derivative - angle between the vector and coordinate axes

Doing an exercise a about directional derivatives, it was required to find the derivative of a given function $f(x,y,z)$ in the direction of the vector $\vec{v}$ that forms with the coordinates axes ...
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### Parametrically defined Spheres in $R^n$

So I have 2 questions here which are closely linked: How do you parametrically define the circle $(x')^2 + (y')^2 = r^2$ using (x') and (y') as coordinates on the plane ax + by + cz = 0 that are ...
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### Trying to find coordinates of another point using bearings

I am trying to help one of my siblings with a trig project and there is one part that I am having a little trouble with. In his project, he is trying to find the coordinates of a UFO given the ...
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### Finding the local extrema of this trigonometric, multivariate function

QUESTION Find all extrema and their places for $$f(x,y) = \mathtt{sin} x + \mathtt{cos} y + \mathtt{cos} (x-y)$$ for $0 \le x \le \frac{\pi}{2}$ and $0 \le y \le \frac{\pi}{2}$ ATTEMPT I go ...
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### Taylor series expansion of $\sec(x +y^2)$
We have $f(x,y) = \sec(x+y^2)$ I want to find the first two non-zero terms of $f$ at $(0,0)$ starting by Taking the first few terms of $\cos x$ centered at zero, $1 - \frac{x^2}{2!}$ Using this ...