How do you use the quadratic formula to solve $3 {sin}^{2} θ - 7 sin θ - 3 = 0$ $3sin^2theta-7sintheta-3=0$ for $0 \leq θ < 360$ $0<=theta<360$ ?

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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

How do you use the quadratic formula to solve 3sin^2theta-7sintheta-3=03sin2θ−7sinθ−3=03sin^2theta-7sintheta-3=0 for 0<=theta<3600≤θ<3600<=theta<360?