Question : If $r\sin\theta=\frac{7}{2}$ and $r\cos\theta=\frac{7\sqrt{3}}{2}$, then the value of $r$ is:
Option 1: 4
Option 2: 3
Option 3: 5
Option 4: 7
New: SSC CHSL Tier 2 answer key released | SSC CHSL 2024 Notification PDF
Recommended: How to crack SSC CHSL | SSC CHSL exam guide
Don't Miss: Month-wise Current Affairs | Upcoming government exams
Correct Answer: 7
Solution :
Given: $r\sin\theta=\frac{7}{2}$ ------(1)
$r\cos\theta=\frac{7\sqrt{3}}{2}$ ------(2)
Squaring and adding both equations, we have:
⇒ $r^{2}\sin^2\theta+r^{2}\cos^{2}\theta=(\frac{7}{2})^{2}+(\frac{7\sqrt{3}}{2})^{2}$
⇒ $r^{2}(\sin^2\theta+\cos^{2}\theta)=\frac{49}{4}+\frac{147}{4}$
⇒ $r^{2}=\frac{196}{4}$
⇒ $r^{2}=49$
$\therefore r=\sqrt{49}=7$
Hence, the correct answer is 7.
Related Questions
Know More about
Staff Selection Commission Combined High ...
Result | Eligibility | Application | Admit Card | Answer Key | Preparation Tips | Cutoff
Get Updates Brochure
Your Staff Selection Commission Combined Higher Secondary Level Exam brochure has been successfully mailed to your registered email id “”.
