The number of values of x in the interval [0, | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Given equation: $3\sin^2 x - 7\sin x + 2 = 0$Factorizing the quadratic equation:$3\sin^2 x - 6\sin x - \sin x + 2 = 0$$3\sin x(\sin x - 2) - 1(\si

Vedclass · Accepted Answer

$6$

Vedclass · Answer

(C) Given equation: $3\sin^2 x - 7\sin x + 2 = 0$Factorizing the quadratic equation:$3\sin^2 x - 6\sin x - \sin x + 2 = 0$$3\sin x(\sin x - 2) - 1(\sin x - 2) = 0$$(3\sin x - 1)(\sin x - 2) = 0$This gives $\sin x = \frac{1}{3}$ or $\sin x = 2$.Since the range of $\sin x$ is $[-1, 1]$,$\sin x = 2$ is not possible.Thus,we solve $\sin x = \frac{1}{3}$.Let $\alpha = \sin^{-1}(\frac{1}{3})$,where $0 In the interval $[0, 5\pi]$,the solutions for $\sin x = \frac{1}{3}$ occur in the following quadrants:In $[0, 2\pi]$,solutions are $\alpha$ and $\pi - \alpha$.In $[2\pi, 4\pi]$,solutions are $2\pi + \alpha$ and $3\pi - \alpha$.In $[4\pi, 5\pi]$,solutions are $4\pi + \alpha$ and $5\pi - \alpha$.Total solutions are $\alpha, \pi - \alpha, 2\pi + \alpha, 3\pi - \alpha, 4\pi + \alpha, 5\pi - \alpha$.There are $6$ such values.

The number of values of $x$ in the interval $[0, 5\pi]$ satisfying the equation $3\sin^2 x - 7\sin x + 2 = 0$ is

Similar Questions

Which of the following compounds when heated with $CO$ at $150^{\circ} C$ and $500 \ atm$ pressure in the presence of $BF_3$ forms ethyl propionate?

Two particles $A$ and $B$ initially at rest move towards each other under a mutual force of attraction. At the instant when the velocity of $A$ is $v$ and that of $B$ is $2v$,the velocity of the centre of mass of the system is

If the length of a stretched string is shortened by $40\%$ and the tension is increased by $44\%$,then the ratio of the final and initial fundamental frequencies is

Which alga exhibits a haplo-diplontic life cycle?

$ABC$ is a triangular plate of uniform thickness. The sides are in the ratio $3:4:5$ as shown in the figure. $I_{AB}, I_{BC}, I_{CA}$ are the moments of inertia of the plate about axes $AB, BC$ and $CA$ respectively. Which one of the following relations is correct?

Vedclass Test Series

Exam Paper Generator

Online Exam Module