Answer
Fill the blanks with:
a.
... x-axis ... $80^{o}$ ... $10^{o}$
b.
... $\sin 80^{o}$ ... $-\sin 10^{o}$
Work Step by Step
Book references:
Reference angle p. 494,
Signs of trig. functions, p.493
a.
The first sentence ends with "... x-axis."
The terminal side of $\theta$=$100^{o}$ and the x-axis form an acute angle of $80^{o}.$
So $\overline{\theta}=80^{o}$.
The terminal side of $\theta$=$190^{o}$ and the x-axis form an acute angle of $10^{o}.$
$\overline{\theta}=10^{o}$
b.
For $100^{o}$, which is in quadrant II,
where sine is positive,
the reference angle is $\overline{\theta}=80^{o}$,
so $\sin 100^{o}=\sin 80^{o}$
For $190^{o}$, which is in quadrant III,
where sine is negative,
the reference angle is $\overline{\theta}=10^{o}$,
so $\sin 190^{o}=-\sin 10^{o}$
Fill the blanks with:
a.
... x-axis ... $80^{o}$ ... $10^{o}$
b.
... $\sin 80^{o}$ ... $-\sin 10^{o}$
