et $$ heta $$ be an angle in standard position. Name the quadrant in which $$ heta $$ lies. $$ \sin heta0, an heta

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et $$ 	heta $$ be an angle in standard position. Name the quadrant in which $$ 	heta $$ lies. $$ \sin 	heta>0, 	an 	heta<0 $$ The angle $$ 	heta $$ lies in which quadrant? II III IV

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To determine the quadrant in which the angle $$ heta $$ lies based on the given conditions $$ \sin heta > 0 $$ and $$ an heta < 0 $$, we can analyze the signs of the trigonometric functions in each quadrant: 1. **Quadrant I**: $$ \sin heta > 0 $$, $$ an heta > 0 $$ 2. **Quadrant II**: $$ \sin heta > 0 $$, $$ an heta < 0 $$ 3. **Quadrant III**: $$ \sin heta < 0 $$, $$ an heta > 0 $$ 4. **Quadrant IV**: $$ \sin heta < 0 $$, $$ an heta < 0 $$ From the conditions: - $$ \sin heta > 0 $$ indicates that $$ heta $$ is in either Quadrant I or Quadrant II. - $$ an heta < 0 $$ indicates that $$ heta $$ is in either Quadrant II or Quadrant IV. The only quadrant that satisfies both conditions is **Quadrant II**. Therefore, the angle $$ heta $$ lies in **Quadrant II**. The angle $$ heta $$ lies in Quadrant II.

et \( \theta \) be an angle in standard position. Name the quadrant in which \( \theta \) lies. \( \sin \theta>0, \tan \theta<0 \) The angle \( \theta \) lies in which quadrant? II III IV

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