Determine the values of $\theta$, where $0 \leq \theta \leq 360$, such that $\sin \theta=-0.6951$. Place numerical value only of theta to the nearest degree in the two blanks with the smaller one first.
A $A$
Answer
The values of \(\theta\) are \(\boxed{136}\) and \(\boxed{316}\) to the nearest degree.
Step 1 ：The sine function has a negative value in the third and fourth quadrants.
Step 2 ：We can find the reference angle in the first quadrant and then find the corresponding angles in the third and fourth quadrants.
Step 3 ：The reference angle can be found by taking the inverse sine (also known as arcsine) of the absolute value of the given sine value.
Step 4 ：We then subtract this reference angle from 180 to find the angle in the third quadrant and subtract it from 360 to find the angle in the fourth quadrant.
Step 5 ：The values of \(\theta\) are \(\boxed{136}\) and \(\boxed{316}\) to the nearest degree.
