Question:
If \(\cos \theta = \dfrac{7}{25}\) and \(\theta\) lies in Quadrant IV, then find the value of \(\sin \theta\).
यदि \(\cos \theta = \dfrac{7}{25}\) और \(\theta\) चतुर्थ चतुर्थांश (Quadrant IV) में स्थित है, तो \(\sin \theta\) का मान ज्ञात कीजिए।
Options:
- \(\dfrac{24}{25}\)
- \(-\dfrac{24}{25}\)
- \(\dfrac{7}{25}\)
- \(-\dfrac{7}{25}\)
- \(\dfrac{24}{25}\)
- \(-\dfrac{24}{25}\)
- \(\dfrac{7}{25}\)
- \(-\dfrac{7}{25}\)
Correct Answer: b)
Explanation:
In Quadrant IV, \(\sin \theta\) is negative.
\(\sin \theta = -\sqrt{1 – \cos^2 \theta} = -\sqrt{1 – \left(\dfrac{7}{25}\right)^2} = -\sqrt{1 – \dfrac{49}{625}} = -\sqrt{\dfrac{576}{625}} = -\dfrac{24}{25}\).
चतुर्थ चतुर्थांश (Quadrant IV) में \(\sin \theta\) ऋणात्मक होता है।
\(\sin \theta = -\sqrt{1 – \cos^2 \theta} = -\sqrt{1 – \dfrac{49}{625}} = -\dfrac{24}{25}\)।