Question

Give the exact intersection point for the equations f(x)=4sin^2x+7sinx+6 and g(x)=2cos^2x-4sinx+11

Ok, my result is that there is no intersection point because if you put f(x)=g(x) and try to solve for x or the intersection point, the LS f(x) is not possible, so there is none?


OK can someone just clarify for me if I have this right? Explain please thanks!

Answer 1

set them equal
2cos^2x-4sinx+11=4sin^2x+7sinx+6
2-2sin^2x-4sinx+11=4sin^2x+7sinx+6
-6sin^2x-11sinx+7=0
check that.
(3sinx+7)(-2sinx+1)=0
sinx=-7/3 not possible
sinx=1/2 x=330deg

check.
f(x)=4(1/4)+7(1/2)+6=10.5
g(x)=2(3/4)-4(1/2)+11=10.5

check me