You can put this solution on YOUR website! given sec theta equals -10 with 180< theta< 270 find and simplify sin theta/2 as an exact value
use x for theta
secx=-10=1/cos
cosx=-1/10=adjacent side/hypotenuse
opposite side=√(10^2-1^2)=√(100-1)=√99
sinx=-√99/10 (in quadrant III where sin<0)
sin(x/2)
=√[(1-cosx)/2]
=√[(1-(-1/10)/2]
=√[(1+(1/10)/2]
=√(1.1/2)
..
check with calculator:
sin^-1(√99/10)=84.26º+180=264.26º(in quadrant III as given)
sin(x/2)=132.13 (in quadrant II where sin>0)
reference angle=132.13-180=47.87º
sin 47.87º≈0.7416..
√(1.1/2)≈0.7416..
(