Published by:
CGP EDU Academic Team
Published on: September 12, 2026
Find 
and 
, if 
and 
lies in the third quadrant.
Text Solution
Verified by ExpertsThe correct answer is:
A
Step 1: We are given that
Step 2: To find sin
Substituting
Step 3: Now, we find tan
Step 4: In conclusion, we have:
cos \theta = -\frac{12}{13}. This indicates that the angle \theta lies in the third quadrant, where cos is negative. Step 2: To find sin
\theta and tan \theta, we can use the Pythagorean identity: sin^2 \theta + cos^2 \theta = 1. Substituting
cos \theta = -\frac{12}{13}: sin^2 \theta + \left(-\frac{12}{13}\right)^2 = 1 sin^2 \theta + \frac{144}{169} = 1 sin^2 \theta = 1 - \frac{144}{169} = \frac{25}{169} sin \theta = -\sqrt{\frac{25}{169}} = -\frac{5}{13} (since it's in the third quadrant, sin is also negative). Step 3: Now, we find tan
\theta: tan \theta = \frac{sin \theta}{cos \theta} = \frac{-\frac{5}{13}}{-\frac{12}{13}} = \frac{5}{12}. Step 4: In conclusion, we have:
sin \theta = -\frac{5}{13}, tan \theta = \frac{5}{12}. Therefore, the answers for sin and tan are found.
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