I'm have a hard time is it none above

Question

Given sin(x) = - 2/7 with 180 deg < x < 270 deg Find sin(2x)

Answer 1

sinx = -2/7 180 deg < x<270 x is in quadrant 3

find sin2x

one way to check your answer or find an answer is use a calculator with an inverse trig function

sinx =-2/7 and x = arcsin(-2/7), so x = about 180+16.6 = 196.6 degrees

then sin2x = sin(2(196.6)) = sin393.2 = sin(393.2-360)= sin33.2 = about .55

another method: use a trig identity and find cosx using the pythagorean theorem

cosx = -sqr(7^2-2^2)/7=-(sqr(49-4))/7=-(sqr45)/7

cosx=-3sqr5)/7

sin2x = 2sinxcosx

= 2(-2/7)(-3sqr5)/7

=12sqr5/49 = an exact solution

= about .55