# What is the period of f(t)=sin( (t)/2 )+ cos( (2t)/5 ) ?

$20 \pi$
Period of $\sin \left(\frac{t}{2}\right)$ --> $2 \left(2 \pi\right) = 4 \pi$
Period of cos $\left(\frac{2 t}{5}\right)$ --> $5 \frac{2 \pi}{2} = \frac{10 \pi}{2} = 5 \pi$
Period of f(t) --> least common multiple of $4 \pi$ and $5 \pi$ -->
$20 \pi$
{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 8, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}