SOLUTION: Find the exact value of cos(t/2) if {{{ tan(t)=12/5 }}} and {{{ pi<t<3pi/2 }}} a) 2 sqrt(13) /13 b) 3 sqrt(13) /13 c) -3/-2 d) -7 sqrt(13) /-13

Algebra ->  Trigonometry-basics -> SOLUTION: Find the exact value of cos(t/2) if {{{ tan(t)=12/5 }}} and {{{ pi<t<3pi/2 }}} a) 2 sqrt(13) /13 b) 3 sqrt(13) /13 c) -3/-2 d) -7 sqrt(13) /-13       Log On


   



Question 928626: Find the exact value of cos(t/2) if
+tan%28t%29=12%2F5+ and +pi%3Ct%3C3pi%2F2+
a) 2 sqrt(13) /13
b) 3 sqrt(13) /13
c) -3/-2
d) -7 sqrt(13) /-13

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

+tan%28t%29=12%2F5+ and +pi%3Ct%3C3pi%2F2+
+tan%5E-1%2812%2F5%29=+1.176 in radians
or
+tan%5E-1%2812%2F5%29=+67.38%B0
then cos%28t%2F2%29=cos%281.176%2F2%29=+cos%280.588%29=0.83205
or
cos%28t%2F2%29=cos%2867.38%2F2%29=+cos%2833.69%29=0.83205
your choices are:
a) 2sqrt%2813%29%2F13=0.5547.........excluded
b) highlight%283sqrt%2813%29%2F13=0.83205%29.......your answer..
c) -3%2F-2=1.5.................excluded
d) -7sqrt%2813%29%2F-13=1.94145.................excluded