Question 925902
Let (t) be a real number with {{{ cos t = 3/7 }}} {{{3pi/2< t < 2pi }}}.
Find the exact value for each of the following:
{{{  sin (t + 3pi/2 ) }}}
{{{  sec (-t)  }}}
{{{  cos (2t)  }}}
{{{  cos ((4pi)/(3) -t) }}}
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reference angle t is in quadrant IV where cos>0, sin<0
cos(t)=3/7
sin(t)=-&#8730;(1-cos^2(t))=-&#8730;(1-(9/49))=-&#8730;(40/49)=-&#8730;40/7
..
sin(t+3&#960;/2)=sin(t)cos(3&#960;/2)+cos(t)sin(3&#960;/2)=-&#8730;40/7*0+3/7*-1=-3/7
..
sec(-t)=1/cos(-t)=1/cos(t)=sec(t)
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cos(2t)=cos^2(t)-sin^2(t)=9/49-40/49=-31/49
..
cos(4&#960;/3-t)=cos(4&#960;/3)cos(t)+sin(4&#960;/3)sin(t)
=-1/2*3/7+-&#8730;3/2*-&#8730;40/7
=-3/14+&#8730;120/14=(-3+&#8730;120)/14