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
New: Unlock 10% OFF on PTE Academic. Use Code: 'C360SPL10'
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.
Candidates can download this e-book to give a boost to thier preparation.
Result | Eligibility | Application | Admit Card | Answer Key | Preparation Tips | Cutoff
Question : If $\sin \theta-\cos \theta=\frac{1}{5}$, then find the value of $\sin \theta+\cos \theta$.
Question : If $\theta$ is an acute angle and $\sin \theta \cos \theta=2 \cos ^3 \theta-\frac{1}{4} \cos \theta$, then the value of $\sin \theta$ is:
Question : If $\sin \theta \cos \theta=\frac{1}{\sqrt{3}}$ then the value of $\left(\sin ^4 \theta+\cos ^4 \theta\right)$ is:
Question : If $\sin \theta \cos \theta=\frac{\sqrt{2}}{3}$,then the value of $\left(\sin ^6 \theta+\cos ^6 \theta\right)$ is:
Question : If $(4 \sin \theta+5 \cos \theta)=3$, then the value of $(4 \cos \theta-5 \sin \theta)$ is:
Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile