Question:
If \(\sin\theta = -\frac{24}{25}\) and \(\theta\) is in the 4th quadrant, \(7\tan\theta + 25\cos\theta\) is equal to
If \(\sin\theta = -\frac{24}{25}\) and \(\theta\) is in the 4th quadrant, \(7\tan\theta + 25\cos\theta\) is equal to
Show Hint
Use quadrant signs carefully for trig functions.
Updated On: Apr 15, 2026
- 17
- -17
- 14
- -14
Show Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
Concept:
\[
\sin^2\theta + \cos^2\theta = 1
\]
Step 1: Find cos.
\[ \cos\theta = \frac{7}{25} \quad (\text{4th quadrant}) \]
Step 2: Find tan.
\[ \tan\theta = \frac{-24}{7} \]
Step 3: Substitute.
\[ 7\tan\theta + 25\cos\theta = 7\left(-\frac{24}{7}\right) + 25\left(\frac{7}{25}\right) \] \[ = -24 + 7 = -17 \]
Step 1: Find cos.
\[ \cos\theta = \frac{7}{25} \quad (\text{4th quadrant}) \]
Step 2: Find tan.
\[ \tan\theta = \frac{-24}{7} \]
Step 3: Substitute.
\[ 7\tan\theta + 25\cos\theta = 7\left(-\frac{24}{7}\right) + 25\left(\frac{7}{25}\right) \] \[ = -24 + 7 = -17 \]
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