Derivative of Cos 2x : Formula, Chain Rule & Proof
Read ArticleCsc Sec Cot - The Reciprocal Trigonometric Functions Explained
Csc, sec, and cot are the three reciprocal trigonometric functions: $\csc\theta = \dfrac{1}{\sin\theta}$, $\sec\theta = \dfrac{1}{\cos\theta}$, and $\cot\theta = \dfrac{1}{\tan\theta}$. This article defines all three, gives their domains, ranges, periods, and graphs, connects them through the Pythagorean identities, and works six examples. For the single-function deep dive, the cosecant page goes further on csc alone.
Read moreCot Pi/6 : Exact Value Root 3 (Unit Circle Proof)
The value of cot pi/6 is exactly $\sqrt{3}$, because $\cot\theta = \dfrac{\cos\theta}{\sin\theta}$ and at $\frac{\pi}{6}$ that ratio is $\dfrac{\sqrt{3}/2}{1/2}$. This article shows the 30-60-90 triangle proof, the unit circle, a standard-angle table, five worked examples, and the mistake that swaps it with tangent.
Read moreCot Pi/4 : Exact Value 1 Explained (Unit Circle)
The value of cot pi/4 is exactly $1$, because $\cot\theta = \dfrac{\cos\theta}{\sin\theta}$ and at $\frac{\pi}{4}$ the sine and cosine are equal. This article shows the 45-45-90 triangle proof, the unit circle, a standard-angle table, five worked examples, and where students slip.
Read moreCot Pi/2 : Exact Value 0 Explained (Unit Circle)
The value of cot pi/2 is exactly $0$, because $\cot\theta = \dfrac{\cos\theta}{\sin\theta}$ and at $\frac{\pi}{2}$ the top of that fraction is $0$. This article shows the unit-circle proof, a standard-angle table, five worked examples, and the mistake that makes students call it undefined.
Read moreCot Pi : Why the Value Is Undefined (Cot π)
The value of cot pi is undefined, because $\cot\theta = \frac{\cos\theta}{\sin\theta}$ and at $\pi$ that becomes $\frac{-1}{0}$, a division by zero. This article explains why it is undefined rather than zero or a clean infinity, ties $\pi$ radians to $180^\circ$, and covers the unit-circle picture, a reference table, examples, and the mistakes students make.
Read moreCot 570 Degrees : Exact Value Is √3 Explained
The value of cot 570 degrees is exactly $\sqrt{3}$, about $1.7321$, because $570^\circ$ is coterminal with $210^\circ$, whose reference angle is $30^\circ$ and whose quadrant keeps cotangent positive. This article shows the coterminal reduction, the reference-angle logic, a reference table, worked examples, and the mistakes students make.
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