Question #28924

1 Answer
turksvids
Jan 19, 2018

#sin(2x)=-24/25#
#cos(2x)=7/25#
#tan(2x)=-24/7#

Explanation:

Since #90^circ < x < 180^circ# and #cosx=-4/5# we know that #sinx = 3/5#. (I drew a triangle to find that.)

#sin(2x)=2sin(x)cos(x) = 2(3/5)(-4/5)=-24/25#.
#cos(2x)=2cos^2(x)-1=2(-4/5)^2-1=2(16/25)-1#
#cos(2x)=7/25#

Since #tan(2x)=sin(2x)/cos(2x)# we know:

#tan(2x)= (-(24/25))/(7/25)=-24/25 * 25/7 = -24/7#.

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