document.write( "Question 716705: f(x)=2sin(1/2x+5pi/6)
\n" ); document.write( "Find five exact value points on the graph \n" ); document.write( "

Algebra.Com's Answer #439944 by jsmallt9(3758) $\"\"$ $\"About$

You can put this solution on YOUR website!
Since all multiples of $\"pi%2F6\"$ are special angles and since the constant part of the argument, $\"5pi%2F6\"$ , is already a multiple of $\"pi%2F6\"$ , it will probably be easiest if we choose values for x that would make the other term in the argument, $\"%281%2F2%29x\"$ , also be a multiple of $\"pi%2F6\"$ . By doing so we would then be able to add the fractions and end up with an argument that is also a multiple of $\"pi%2F6\"$ .

\n" ); document.write( "Perhaps you can already tell what values x should have that would turn $\"%281%2F2%29x\"$ into a multiple of $\"pi%2F6\"$ . If not, then just pick a multiple of $\"pi%2F6\"$ , set $\"%281%2F2%29x\"$ equal to it and solve for x. Let's be easy on ourselves and choose $\"pi%2F6\"$ itself:
\n" ); document.write( " $\"%281%2F2%29x+=+pi%2F6\"$
\n" ); document.write( "Multiplying both sides by 6 we get:
\n" ); document.write( " $\"3x+=+pi\"$
\n" ); document.write( "Dividing by 3 we get:
\n" ); document.write( " $\"x+=+pi%2F3\"$

\n" ); document.write( "Perhaps you can now see that if x is any multiple of $\"pi%2F3\"$ , then $\"%281%2F2%29x\"$ would end up being some multiple of $\"pi%2F6\"$ . I'll get you started on a table of values:
\n" ); document.write( "

\r\n" );
document.write( "  x    (1/2)x   (1/2)x+5pi/6  sin((1/2)x+5pi/6)   2sin((1/2)x+5pi/6)   f(x)\r\n" );
document.write( "pi/3    pi/6      6pi/6 = pi        0                  0                0\r\n" );
document.write( "-pi/3   -pi/6   4pi/6 = 2pi/3     sqrt(3)/2            sqrt(3)         sqrt(3)\r\n" );
document.write( "  0       0         5pi/6          1/2                 1                1\r\n" );
document.write( "

I'll leave it up to you to find two more.

\n" ); document.write( "P.S. We did not have to make x be a value that made the argument of sin be a multiple of pi/6. We just did that because it made things easier. Any x that would make (1/2)x+5pi/6 turn out to be any of the special angles would work. \n" ); document.write( "

\n" );