Articles of angle

We have angle=arctan(dy/dx), but what happens when dx=0?

Here is a formula: $\text{angle}=\arctan(dy/dx)$. I can find an angle with my calculator for any value except $dx=0$. My question is: is there no angle or, is there something that says when $dx=0$ the angle is found differently?

Quaternion – Angle computation using accelerometer and gyroscope

I have been using a 6dof LSM6DS0 IMU unit (with accelerometer and gyroscope) and am trying to calculate the angle of rotation around all three axes. I have tried many methods but am not getting the results as expected. Methods tried: (i) Complementary filter approach – I am able to get the angles using the […]

Product Identity Multiple Angle or $\sin(nx)=2^{n-1}\prod_{k=0}^{n-1}\sin\left(\frac{k\pi}n+x\right)$

This question already has an answer here: Proof of $\sin nx=2^{n-1}\prod_{k=0}^{n-1} \sin\left( x + \frac{k\pi}{n} \right)$ 1 answer

Find the bearing angle between two points in a 2D space

I continue developing a 2D Collision Detection System in a programming language (Javascript) and one of the last things I need to sharpen it is to know a formula to find this angle: NOTE: X and Y increase their value FROM LEFT TO RIGHT AND TOP TO BOTTOM As you can see the angle is […]

What is the advantage of measuring an angle in radian(s)?

This question already has an answer here: Why is radian so common in maths? 14 answers

calculating angle in circle

How to calculate angle in a circle. Please see the diagram to get the idea what I want to calculate? I have origin of circle that is $(x_1,x_2)$. I have a point on circumstance of circle that is $(x_2,y_2)$. Also I know the radius of circle that is R. How to calculate the angle between […]

Why in calculus the angles are measured in radians?

This question already has an answer here: Why does the derivative of sine only work for radians? 17 answers Why do we require radians in calculus? 10 answers

Show that the angles satisfy $x+y=z$

How can I show that $x+y=z$ in the figure without using trigonometry? I have tried to solve it with analytic geometry, but it doesn’t work out for me.

Determine angle $x$ using only elementary geometry

Using only elementary geometry, determine angle x. You may not use trigonometry, such as sines and cosines, the law of sines, the law of cosines, etc.

“World's Hardest Easy Geometry Problem”

This question is a “corollary” (if you will) to the World’s Hardest Easy Geometry Problem (external website). Formally, this is called Langley’s Problem. The objective of that problem was to solve for angle $x^{\circ}$, with the given angles of $10^{\circ}, 70^{\circ}, 60^{\circ}, 20^{\circ}$. Someone presented a solution to that problem. Here’s also a rather colorful […]