[amp_mcq option1=”1″ option2=”2″ option3=”3″ option4=”4 or more” correct=”option1″]<\/p>\n
The correct answer is $\\boxed{\\text{B}}$.<\/p>\n
The equation $\\sin(x) = \\frac{x}{2}$ has two distinct solutions in the interval $[0, 2\\pi]$. These solutions are $x = \\frac{\\pi}{6}$ and $x = \\frac{5\\pi}{6}$.<\/p>\n
To see this, we can use the graph of the sine function. The graph of the sine function is shown below.<\/p>\n
[asy]
\nunitsize(1 cm);<\/p>\n
draw((0,-1.2)–(0,1.2));
\ndraw((0,0)–(2*pi,0));<\/p>\n
real ticklen=0.1;
\nreal tickspace=0.2;
\nreal axisarrowsize=0.14inch;<\/p>\n
real ticklength=0.1cm;
\nreal vectorarrowsize=0.2cm;<\/p>\n
draw((0,-1.2)–(0,1.2));
\ndraw((0,0)–(2*pi,0));<\/p>\n
label(“$x$”, (2*pi,0), S);
\nlabel(“$y$”, (0,1.2), E);<\/p>\n
real i;
\nfor (i=-pi; i<pi; i+=pi\/4) {
\n draw((i,-0.1)–(i,0.1));
\n}<\/p>\n
real j;
\nfor (j=-1.2; j<1.2; j+=0.2) {
\n if (j>-0.1 && j<0.1) continue;
\n draw((0,j)–(0.1,j));
\n}<\/p>\n
dot(“$\\frac{\\pi}{6}$”, (pi\/6,0.1), S);
\ndot(“$\\frac{5\\pi}{6}$”, (5*pi\/6,0.1), S);
\n[\/asy]<\/p>\n
The graph intersects the line $y = \\frac{x}{2}$ at $x = \\frac{\\pi}{6}$ and $x = \\frac{5\\pi}{6}$. Therefore, these are the two distinct solutions to the equation $\\sin(x) = \\frac{x}{2}$ in the interval $[0, 2\\pi]$.<\/p>\n","protected":false},"excerpt":{"rendered":"
[amp_mcq option1=”1″ option2=”2″ option3=”3″ option4=”4 or more” correct=”option1″]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[690],"tags":[],"class_list":["post-20200","post","type-post","status-publish","format-standard","hentry","category-calculus","no-featured-image-padding"],"yoast_head":"\n