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Completion requirements
Given the reference angle of \(35^\circ\), determine the angles in
standard position where tan \(\theta\) is negative, for \(0^\circ \le
\theta < 360^\circ \).
Now that you are familiar with exact values and the CAST rule, and you have worked with special right triangles and their corresponding exact value trigonometric ratios, you can determine the trigonometric ratios for angles in standard position terminating in any quadrant.
Using CAST, the tangent ratio is negative in Quadrants II and IV. Therefore the angles are:
\(\begin{align}
180^\circ - \theta &= \theta _R \\
180^\circ - \theta &= 35^\circ \\
180^\circ - 35^\circ &= \theta \\
145^\circ &= \theta \\
\end{align}\)
180^\circ - \theta &= \theta _R \\
180^\circ - \theta &= 35^\circ \\
180^\circ - 35^\circ &= \theta \\
145^\circ &= \theta \\
\end{align}\)
\(\begin{align}
360^\circ - \theta &= \theta _R \\
360^\circ - \theta &= 35^\circ \\
360^\circ - 35^\circ &= \theta \\
325^\circ &= \theta \\
\end{align}\)
360^\circ - \theta &= \theta _R \\
360^\circ - \theta &= 35^\circ \\
360^\circ - 35^\circ &= \theta \\
325^\circ &= \theta \\
\end{align}\)