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Geometry

Graphs of Trigonometric Functions

Graphs of Trigonometric Functions: Level 3 Challenges

         

f(x)=sin⁡6x+cos⁡6x+sin⁡4xcos⁡2x+cos⁡4xsin⁡2x\large \color{orangered}{f(x)=\sin^6x+\cos^6x+\sin^4x \cos^2x + \cos^4x \sin^2x} Find the fundamental period of the function f(x)\color{orangered}{f(x)}.

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Sandeep Bhardwaj by Sandeep Bhardwaj

Over the entire real line, the number of values of x where the function

f(x)=cos⁡x+cos⁡(2x) f(x) = \cos x + \cos ( \sqrt{2}x ) attains its maximum value is:

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Ali Khan by Ali Khan

{y=sin⁡(x)y=cos⁡(x)y=tan⁡(x)y=csc⁡(x) \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=0x = 0 to x=π2x = \frac \pi2 .

If a vertical line is drawn where the graphs of y=cos⁡(x)y=\cos (x) and y=tan⁡(x)y = \tan (x) intersect, this line intersects the graphs of y=sin⁡(x)y=\sin(x) and y=csc⁡(x)y=\csc(x) at points AA and BB. What is the distance between AA and BB?

Avn Bha by avn bha

How many real numbers xx satisfy sin⁡x=x100?\sin x = \frac{x}{100}?

Poetri Sonya by Poetri Sonya

What is the smallest positive integer nn such that f(x)=sin⁡(sin⁡(nx))tan⁡(xn)\large \displaystyle f(x)= \frac {\sin(\sin (nx))}{\tan \left(\frac{x}{n}\right) } has a fundamental period of 6π?6\pi?

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Keshav Tiwari by Keshav Tiwari
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