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

Algebra ->  Trigonometry-basics -> 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      Log On


   

Question 925902: Let (t) be a real number with +cos+t+=+3%2F7+ 3pi%2F2%3C+t+%3C+2pi+.
Find the exact value for each of the following:
++sin+%28t+%2B+3pi%2F2+%29+
++sec+%28-t%29++
++cos+%282t%29++
++cos+%28%284pi%29%2F%283%29+-t%29+

THANK YOU!
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Let (t) be a real number with +cos+t+=+3%2F7+ 3pi%2F2%3C+t+%3C+2pi+.
Find the exact value for each of the following:
++sin+%28t+%2B+3pi%2F2+%29+
++sec+%28-t%29++
++cos+%282t%29++
++cos+%28%284pi%29%2F%283%29+-t%29+
***
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