Question 1040749
The basic facts you need to know about
the sine curve is:
(1) {{{ sin(x) }}} repeats itself every {{{ 2pi }}}
radians
(2) the maximum value of {{{ sin(x) }}} is {{{ 1 }}}
and this maximum occurs every {{{ pi/2 +- 2pi }}}
radians
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(i), (ii), and (iii)
You are given the interval −π ≤ x ≤ &#960
so, the only place where there is a maximum in this
interval is: {{{ x = pi/2 }}}
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Your sine function is {{{ 3*sin( x ) }}}, the the maximum is
{{{ 3*1 = 3 }}}. Now you know the maximum point is at 
( pi/2, 3 )
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The straight line {{{ y = k*x }}} must also pass through that
point and also (0,0) since {{{ y = k*0 }}} gives you (0,0)
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The slope, {{{ k }}}, is {{{ ( 3 - 0 ) / ( pi/2 - 0 ) = 6/pi }}}, so the equation is:
{{{ y = ( 6/pi)*x }}}
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Here are plots of
{{{ y = 3*sin(x) }}} and
{{{ y = ( 6/pi )*x }}}

{{{ graph( 400, 800, -pi, pi, -4, 4, 3*sin(x) , (6/pi)*x ) }}}