Question 1136950
A is an obtuse angle such that cos(A)=-4/5. Find:

1. Cos(4A)
<pre>
A is a QII angle.  We draw a 3-4-5 right triangle in QII.

{{{drawing(200,200,-5,5,-5,5,line(-6,0,6,0),line(0,-6,0,6),
green(triangle(-4,0,-4,3,0,0),locate(-3,0,x=-4),locate(-5,1.7,y=3),locate(-2,1.8,r=5)), red(arc(0,0,2,-2,0,144),locate(.1,1.63,A))

  )}}}

{{{cos(A)=x/r=(-4)/5=-4/5}}}, {{{sin(A)=y/r=3/5}}},

{{{cos(2A)=2cos^2(A)-1=2(-4/5)^2-1=2(16/25)-1=32/25-25/25=7/25}}}

{{{cos(4A)=2cos^2(2A)-1=2(7/25)^2-1=2(49/625)-1=98/625-625/625=-527/625}}}
</pre>
2. Sin (4A).
<pre>
{{{sin(2A)=2sin(A)cos(A)=2(3/5)(-4/5)=-24/25}}}

{{{sin(4A)=2sin(2A)cos(2A)=2(-24/25)(7/25)=-336/625}}}

Edwin</pre>