If log _{1/sqrt{2}} sin x 0 for x in [0, 4p | vedclass

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

Question

(A) Given the inequality $\log _{1/\sqrt{2}} \sin x > 0$.Since the base $1/\sqrt{2}$ is between $0$ and $1$,the inequality reverses when we remove the

Vedclass · Accepted Answer

$4$

Vedclass · Answer

(A) Given the inequality $\log _{1/\sqrt{2}} \sin x > 0$.Since the base $1/\sqrt{2}$ is between $0$ and $1$,the inequality reverses when we remove the logarithm:$0 $0 We need to find the values of $x = k \cdot \frac{\pi}{4}$ for $k \in \mathbb{Z}$ in the interval $[0, 4\pi]$ such that $0 The multiples of $\frac{\pi}{4}$ in $[0, 4\pi]$ are $0, \frac{\pi}{4}, \frac{2\pi}{4}, \frac{3\pi}{4}, \dots, \frac{16\pi}{4}$.Values where $\sin x = 0$ or $\sin x = 1$ must be excluded.For $x \in [0, 4\pi]$,$\sin x = 0$ at $x = 0, \pi, 2\pi, 3\pi, 4\pi$.$\sin x = 1$ at $x = \frac{\pi}{2}, \frac{5\pi}{2}$.Checking multiples of $\frac{\pi}{4}$:$x = \frac{\pi}{4} (\sin > 0), \frac{2\pi}{4} (\sin = 1, 	ext{exclude}), \frac{3\pi}{4} (\sin > 0), \frac{4\pi}{4} (\sin = 0, 	ext{exclude}), \frac{5\pi}{4} (\sin  0), \frac{10\pi}{4} (\sin = 1, 	ext{exclude}), \frac{11\pi}{4} (\sin > 0), \frac{12\pi}{4} (\sin = 0, 	ext{exclude}), \frac{13\pi}{4} (\sin The valid values are $\frac{\pi}{4}, \frac{3\pi}{4}, \frac{9\pi}{4}, \frac{11\pi}{4}$.There are $4$ such values.

If $\log _{1/\sqrt{2}} \sin x > 0$ for $x \in [0, 4\pi]$,then the number of values of $x$ which are integral multiples of $\frac{\pi}{4}$ is:

Similar Questions

The number of solutions of $\log_{4}(x - 1) = \log_{2}(x - 3)$ is:

Evaluate: $\log _7(\log _7\sqrt {7\sqrt {7\sqrt 7 } }) = $

$e^{\left(\sec h^{-1} \frac{1}{2}+\tan h^{-1} \frac{1}{2}+\sin h^{-1} \frac{1}{2}\right)}=$

$\log (9+3 \sqrt{2}(2+\sqrt{5})+4 \sqrt{5})=$

If $\log_{10} 2 = 0.30103$ and $\log_{10} 3 = 0.47712$,then the number of digits in $3^{12} \times 2^8$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module