Answer
a) $48.6^{\circ} + 360^{\circ}k$ and $131.4^{\circ} + 360^{\circ}k$, for all integers $k$.
b) $\theta = 48.6˚, 131.4˚$
Work Step by Step
b) $4sin\theta - 3 = 0$
$4sin\theta = 3$
$sin\theta = \frac{3}{4}$
by GDC / calculator
$\theta = sin^{-1}(0.75)$
$\theta = 48.59˚$
$\theta = 48.6˚$
But there are two answers, since $sin\theta$ is positive in both quadrant I and II. $= 180 - 48.6$
$= 131.4˚$
Therefore, $\theta = 48.6˚, 131.4˚$
a) Take the two angles and add $360^{\circ}k$for all integers $k$, to find all degree solutions.
$48.6^{\circ} + 360^{\circ}k$ and $131.4^{\circ} + 360^{\circ}k$, for all integers $k$.
