$\sin x^{\circ} = 0.66913$ Given that $x$ is an obtuse angle, find $x$. Answer x = ... $\cos y^{\circ} = -\cos 121^{\circ}$ Given that $y$ is an acute angle, find the value of $y$. Answer y = ...

1. Find the acute angle with sine $0.66913$, then convert to the obtuse angle.

$\sin^{-1}(0.66913) \approx 42^\circ$

Since $x$ is obtuse and $\sin x^\circ$ is positive,

$x = 180^\circ - 42^\circ = 138^\circ.$

1. Use the cosine relationship between supplementary angles to find the acute angle.

Since $121^\circ$ is obtuse,
$\cos 121^\circ = -\cos(180^\circ-121^\circ)=-\cos 59^\circ.$
Hence
$-\cos 121^\circ=\cos 59^\circ.$
So
$\cos y^\circ=\cos 59^\circ.$
Since $y$ is acute, $y=59^\circ.$