Math  /  Trigonometry

QuestionFind θ\theta such that 4sin2θ4=14 \sin^{2} \theta - 4 = -1 for 0θ3600^{\circ} \leq \theta \leq 360^{\circ}.

Studdy Solution
Now we need to find the values of θ\theta in the range 0θ3600^{\circ} \leq \theta \leq360^{\circ} for which sinθ=32\sin \theta = \frac{\sqrt{3}}{2} or sinθ=32\sin \theta = -\frac{\sqrt{3}}{2}.
From the unit circle or sine graph, we know that sinθ=32\sin \theta = \frac{\sqrt{3}}{2} at θ=60\theta =60^{\circ} and θ=120\theta =120^{\circ}, and sinθ=32\sin \theta = -\frac{\sqrt{3}}{2} at θ=240\theta =240^{\circ} and θ=300\theta =300^{\circ}.
So, the solutions to the equation are θ=60,120,240,300\theta =60^{\circ},120^{\circ},240^{\circ},300^{\circ}.

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