Let $$ \theta $$ be an angle in standard poshtion. Name the quadrant in which $$ \theta $$ lies. $$ \tan \theta

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Let $$ \theta $$ be an angle in standard poshtion. Name the quadrant in which $$ \theta $$ lies. $$ \tan \theta<0, \cos \theta<0 $$

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- Since $$ an heta < 0 $$ and $$ \cos heta < 0 $$, we begin by analyzing the quadrants where these conditions hold. - In standard position, recall that: - $$ an heta = \frac{\sin heta}{\cos heta} $$. For $$ an heta < 0 $$, the sine and cosine must have opposite signs. - The cosine is negative in the second and third quadrants. - Consider each quadrant: - **Quadrant II:** - $$ \sin heta > 0 $$ - $$ \cos heta < 0 $$ - Thus, $$ an heta = \frac{\sin heta}{\cos heta} < 0 $$ - **Quadrant III:** - $$ \sin heta < 0 $$ - $$ \cos heta < 0 $$ - Thus, $$ an heta = \frac{\sin heta}{\cos heta} > 0 $$ - The only quadrant that satisfies both $$ an heta < 0 $$ and $$ \cos heta < 0 $$ is **Quadrant II**. $$ heta $$ lies in Quadrant II.

Let \( \theta \) be an angle in standard poshtion. Name the quadrant in which \( \theta \) lies. \[ \tan \theta<0, \cos \theta<0 \]

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