Graphs of Trigonometric Functions
\[\large \color{orangered}{f(x)=\sin^6x+\cos^6x+\sin^4x \cos^2x + \cos^4x \sin^2x}\] Find the fundamental period of the function \(\color{orangered}{f(x)}\).
by
Sandeep Bhardwaj
Over the entire real line, the number of values of x where the function
\[ f(x) = \cos x + \cos ( \sqrt{2}x ) \] attains its maximum value is:
by
Ali Khan
\[ \large \begin{cases}{y=\sin (x)} \\ {y=\cos (x)} \\ {y=\tan (x)} \\ {y=\csc (x)}\end{cases} \]
The four graphs above are drawn on the same axes from \(x = 0 \) to \(x = \frac \pi2 \).
If a vertical line is drawn where the graphs of \(y=\cos (x) \) and \(y = \tan (x)\) intersect, this line intersects the graphs of \(y=\sin(x)\) and \(y=\csc(x)\) at points \(A\) and \(B\). What is the distance between \(A\) and \(B\)?
by
avn bha
How many real numbers \(x\) satisfy \(\sin x = \frac{x}{100}?\)
by
Poetri Sonya
What is the smallest positive integer \(n\) such that \[\large \displaystyle f(x)= \frac {\sin(\sin (nx))}{\tan \left(\frac{x}{n}\right) } \] has a fundamental period of \(6\pi? \)
by
Keshav Tiwari