Example 2
Completion requirements
| Example 2 |
Determine all the angles in standard position, for \(0^\circ \le \theta < 360^\circ \), that have a reference angle of \(35^\circ\).
Calculate the angle in each quadrant individually.
Quadrant I: \(\theta _R = \theta \)
\(\begin{align}
\theta _R &= \theta \\
35^\circ &= \theta \\
\end{align}\)
Quadrant II: \(\theta _R = 180^\circ - \theta \)
\(\begin{align}
\theta _R &= 180^\circ - \theta \\
35^\circ &= 180^\circ - \theta \\
-145^\circ &= - \theta \\
145^\circ &= \theta \\
\end{align}\)
Quadrant III: \(\theta _R = \theta - 180^\circ \)
\(\begin{align}
\theta _R &= \theta - 180^\circ \\
35^\circ &= \theta - 180^\circ \\
215^\circ &= \theta \\
\end{align}\)
Quadrant IV: \(\theta _R = 360^\circ - \theta \)
\(\begin{align}
\theta _R &= 360^\circ - \theta \\
35^\circ &= 360^\circ - \theta \\
-325^\circ &= - \theta \\
325^\circ &= \theta \\
\end{align}\)
Quadrant I: \(\theta _R = \theta \)
\(\begin{align}
\theta _R &= \theta \\
35^\circ &= \theta \\
\end{align}\)
Quadrant II: \(\theta _R = 180^\circ - \theta \)
\(\begin{align}
\theta _R &= 180^\circ - \theta \\
35^\circ &= 180^\circ - \theta \\
-145^\circ &= - \theta \\
145^\circ &= \theta \\
\end{align}\)
Quadrant III: \(\theta _R = \theta - 180^\circ \)
\(\begin{align}
\theta _R &= \theta - 180^\circ \\
35^\circ &= \theta - 180^\circ \\
215^\circ &= \theta \\
\end{align}\)
Quadrant IV: \(\theta _R = 360^\circ - \theta \)
\(\begin{align}
\theta _R &= 360^\circ - \theta \\
35^\circ &= 360^\circ - \theta \\
-325^\circ &= - \theta \\
325^\circ &= \theta \\
\end{align}\)