Property 13
The Graphs of Trigonometric Functions
Sinus
Cosinus
Tangent
Cotangent
The Period of Trigonometric Functions
\(k,a,b\in\mathbb R\)
\(f(x)=k\cdot\sin^n(ax+b)\)
\(\longrightarrow P=\samefrac{2\pi}{|a|}\quad\text{(If n is odd)}\)
\(\longrightarrow P=\samefrac\pi{|a|}\quad\text{(If n is even)}\)
\(f(x)=k\cdot\cos^n(ax+b)\)
\(\longrightarrow P=\samefrac{2\pi}{|a|}\quad\text{(If n is odd)}\)
\(\longrightarrow P=\samefrac\pi{|a|}\quad\text{(If n is even)}\)
\(f(x)=k\cdot\tan^n(ax+b)\longrightarrow P=\samefrac\pi{|a|}\)
\(f(x)=k\cdot\cot^n(ax+b)\longrightarrow P=\samefrac\pi{|a|}\)
\(f(x)=h(x)+g(x)\)
\(h(x)\longrightarrow T_1\text{ (T₁ period)}\)
\(g(x)\longrightarrow T_2\text{ (T₂ period)}\)
OKEK (T₁,T₂) is the period of f(x))
Find the principle periods of the given functions below.
1.
\(f(x)=\cos^4(3x-2)\)
2.
\(f(x)=\sin(6x-2)\)
3.
\(f(x)=\sin^6(4x-2)\)
4.
\(f(x)=\samefrac23+2\tan^3(6x-1)\)
5.
\(f(x)=\cot^4(8x-1)\)
6.
\(f(x)=\sin^4(5x+1)+\cot(3x+4)\)