SOLUTION: 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) }}}
{{{ c
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Question 925902: Let (t) be a real number with .
Find the exact value for each of the following:
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Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
Let (t) be a real number with .
Find the exact value for each of the following:
***
reference angle t is in quadrant IV where cos>0, sin<0
cos(t)=3/7
sin(t)=-√(1-cos^2(t))=-√(1-(9/49))=-√(40/49)=-√40/7
..
sin(t+3π/2)=sin(t)cos(3π/2)+cos(t)sin(3π/2)=-√40/7*0+3/7*-1=-3/7
..
sec(-t)=1/cos(-t)=1/cos(t)=sec(t)
..
cos(2t)=cos^2(t)-sin^2(t)=9/49-40/49=-31/49
..
cos(4π/3-t)=cos(4π/3)cos(t)+sin(4π/3)sin(t)
=-1/2*3/7+-√3/2*-√40/7
=-3/14+√120/14=(-3+√120)/14
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