How do you use the quadratic formula to solve #3sin^2theta-7sintheta-3=0# for #0<=theta<360#?

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Answer 1 · 2016-12-16T08:14:58

The answer is #S={201.7º,338.3º}#

The quadratic equation is #ax^2+bx+c=0#

In our case #x=sintheta#

#3sin^2theta-7sintheta-3=0#

Lets calculate the discriminant

#Delta=b^2-4ac=(-7)^2-4(3)(-3)=85#

As #Delta>0#, we have 2 real roots

#sintheta=(-b+-sqrtDelta)/(2a)#

#=(7+-sqrt85)/6#

#sin theta=(7+sqrt85)/6=2.7# , so no solution as #-1<=sintheta<=1#

#sin theta=(7-sqrt85)/6=-0.37#

#theta=201.7#º and #=338.3#º