Answer
a) $194.5^{\circ} + 360^{\circ}k$ and $345.5^{\circ} + 360^{\circ}k$, for all integers $k$.
b) $\theta = 194.5˚, 345.5˚$.
Work Step by Step
b) $4sin\theta + 3 = 0$
$4sin\theta = -3$
$sin\theta = -\frac{3}{4}$
There are two answers in QIII and QIV as $sin\theta$ is negative in both of those quadrants.
We first get the angle of $\theta = sin^{-1}(-\frac{3}{4}) = -14.5˚$, but we'll use $14.5˚$ as the reference angle. Knowing that $sin\theta$ is negative, we only look at QIII and QIV. QIII:
$\theta = 180 + 14.5$
$\theta = 194.5˚$
QIV: $\theta = 360 - 14.5$
$\theta = 345.5˚$
Therefore, $\theta = 194.5˚, 345.5˚$.
a) Take the two angles and add $360^{\circ}k$for all integers $k$, to find all degree solutions.
$194.5^{\circ} + 360^{\circ}k$ and $345.5^{\circ} + 360^{\circ}k$, for all integers $k$.
