Evaluate the following expression for sine value?

Question

$sin^2theta -sin^4 theta = 3/16$

1232 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-08-08T15:31:04

$+- 1/2 +- 1/2 sqrt3$

$3/16 = sin^2theta - sin^4theta = sin^2theta ( 1 - sin^2theta)$

$= sin^2theta cos^2theta = 1/4 sin^2 2theta$

So,

$sin^2 2theta = 3/4 rArr sin 2theta = +-1/2 sqrt 3 = sin ( +_ pi/3)$

$2theta = kpi + (-1)^k ( +-pi/3) rArr theta = k/2pi +(-1)^k(+-pi/6)$

$rArr sin theta = sin ( kpi/2 + (-1)^k ( +-pi/6)), k =0, +-1, +-2, +-3,,,$

$= repetitive { sin ( -2/3pi ) sin ( 1/6pi ) sin ( -1/6pi) sin (2/3pi }$

# = { +-1/2 +-sqrt3/2 }

graph{ y-x^2+x^4+3/16=0[-1 1 -.01 .01]}

x-intercepts are the sine values.