Question

Solve sin^2θ−4sinθ−5=0 for 0°≤θ≤360°

Answer 1

`\theta=270^\circ`

Explanation:

Given Equation and Parameters

`sin^2\theta-4sin\theta-5=0,\: 0^\circ\leq\theta\leq 360^\circ`

Calculation

Let
`u=sin\theta`, thus:

`u^2-4u-5=0\\\\(u+1)(u-5)=0\\\\u=-1,\: u=5`

`sin\theta=-1\\\\\theta=270^\circ`

`sin\theta=5\\\\\theta=unde fined`

Conclusion

`\theta=270^\circ`