Given y=atan(x)/x, how can I get “x” for a given value of “y”?

I have a simple C++ equation that I’m using to perform lens distortion correction. $$y=\frac{\arctan(x)}{x}$$ where $x$ is in radians between 0.0 and 1.0. I’m trying to come up with the inverse of this equation [get $x$ given $y$] but I’ve been unsuccessful. I got this far before my flabby math skills were exhausted: $$xy … Read more

trigonometry of interfering waves

I have a book which makes the following claim: Acos(ωt+ϕ)=A1cos(ωt+ϕ1)+A2cos(ωt+ϕ2) …where: A2=A21+A22+2A1A2cos(ϕ1−ϕ2) …and: tan(ϕ)=A1sin(ϕ1)+A2sin(ϕ2)A1cos(ϕ1)+A2cos(ϕ2) However, I’ve been unable to derive this set of relations, and I’ve used every trig identity I’ve been able to think of. Either I’m missing something, or there’s a simplifying assumption or approximation the author is making that they aren’t explicitly … Read more

Why cant I solve the equation 4\sin(2x)\cdot \cos(2x)=2\cos(2x)4\sin(2x)\cdot \cos(2x)=2\cos(2x) by dividing both sides by \cos(2x)\cos(2x)??

This assignment assumes the domain is [0, \pi]. Why can’t I solve the following equation by dividing both sides by \cos(2x)? 4\sin(2x)\cdot \cos(2x)=2\cos(2x) If I would continue to do so, wouldn’t \cos(2x) cancel out on both sides, leaving me with 4\sin(2x)=2 Which will then be solvable. According to khanacademy’s answer it seems like I would … Read more

sin(π−a)=sin(a)\sin(\pi – a) = \sin (a). How/why? [closed]

Closed. This question is off-topic. It is not currently accepting answers. Want to improve this question? Update the question so it’s on-topic for Mathematics Stack Exchange. Closed 7 years ago. Improve this question Can someone please explain how and why sin(π−a)=sin(a)? The handout from class doesn’t really explain it. I tried asking the teach but … Read more

Trigonometry Identity (Proving)

How to prove this identity? cos2α+cos2β1+cos2(α+β)=cos(α−β)cos(α+β) I’ve tried solving from L.H.S and R.H.S. But failed. Anyone can guide me? Thanks. Answer The sum to product formula is cos2α+cos2β=2cos2α+2β2cos2α−2β2=2cos(α+β)cos(α−β) Next cos2(α+β)=2cos2(α+β)−1 AttributionSource : Link , Question Author : Mathxx , Answer Author : egreg

How do I solve this trigonometric equation? [closed]

Closed. This question is off-topic. It is not currently accepting answers. Want to improve this question? Update the question so it’s on-topic for Mathematics Stack Exchange. Closed 6 years ago. Improve this question Solve the equation sin(3π10−x2)=12sin(π10+3×2). I tried applying some Ratio properties, but they just made the equation nasty. Some hints please. Thanks. Answer … Read more

Function that graphs repeating upper halves of circles

I’m trying to write a periodic function that repeats the upper half of a unit circle, so it would look similar to $|\cos(x)|$ but with the upper half of a circle instead. If anyone could help me out it would be much appreciated. Answer This does the trick: $$y = \sqrt{1-\left(\frac{\arccos \left(\cos \left(\pi x\right)\right)}{\pi }\right)^2}$$ … Read more

About the convexity of sinx\sin x for π≤x≤2π\pi\leq x\leq 2\pi [closed]

Closed. This question is off-topic. It is not currently accepting answers. Want to improve this question? Update the question so it’s on-topic for Mathematics Stack Exchange. Closed 6 years ago. Improve this question To prove the convexity of sinx over [π,2π] through the second derivative is easy, but I would be interested in a (possibly) … Read more

How to find if a point is outside a circle circumference area?

I’d like to know if it’s possible to calculate if a point is inside or outside the circle circumference area based on it’s $x$ and $y$ values ? Example, $(x, y)= (0.85, -0.9)$ and the radius is $1$ Answer You need only calculate the distance between $(x_1, y_1)$ (the point in question) and $(x_0, y_0)$ … Read more