Help please?

Question

468 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-03-02T16:40:13

The solution is #"option (a)"#, #S={203.6^@, 336.4^@ }#

The quadratic equation in #sintheta# is

#5sin^2theta-18sintheta-8=0#

Compare this equation to the quadratic equation

#ax^2+bx+c=0#

#a=5#

#b=-18#

#c=-8#

The discriminant is

#Delta=b^2-4ac=(-18)^2-4(5)(-8)=484#

As, #Delta>0#, we expect #2# real solutions

#sintheta=((-b)+-sqrtDelta)/(2a)=(-(-18+-sqrt(484)))/(2*5)#

#=(18+-22)/(10)#

#sintheta=4#, there are no solutions since #-1<=sinx<=1#

#sintheta=-4/10=-0.4#

#theta=336.4^@# and #x=203.6^@#