Answer
a) $228.6^{\circ} + 360^{\circ}k$ and $311.4^{\circ} + 360^{\circ}k$, for all integers $k$.
b) $\theta = 228.6˚, 311.4˚$
Work Step by Step
b) $sin\theta - 3 = 5sin\theta$
$sin\theta - 5sin\theta = 3$
$-4sin\theta = 3$
$sin\theta = -\frac{3}{4}$
$\theta = -48.6˚$
Use $48.6˚$ as the reference angle. And recall that $sin\theta$ is negative in only QIII and QIV. QIII:
$\theta = 180 + 48.6$
$\theta = 228.6˚$
QIV: $\theta = 360 - 48.6$
$\theta = 311.4˚$
Therefore, $\theta = 228.6˚, 311.4˚$
a) Take the two angles and add $360^{\circ}k$for all integers $k$, to find all degree solutions.
$228.6^{\circ} + 360^{\circ}k$ and $311.4^{\circ} + 360^{\circ}k$, for all integers $k$.
