Period of Trigonometric Ratios

Q. The period of the curve $y=\sin 4x$ is equal to

1. $e^{\ln \sqrt{\frac{{\pi }^2}{4}}}$
2. $e^{\ln \left|\frac{\pi }{4}\right|}$
3. $e^{\frac{1}{2}\ln \left(\frac{{\pi }^2}{16}\right)}$
4. Period of $y=\cos 4x$

Q.

Which transformation causes the described change in the graph of function $y=\cos \left(x\right)$?

The transformation __ results in vertical stretch.

1. $\frac{1}{3}\cos \left(x\right)$

2. $\cos \left(x+4\right)$

3. $\cos \left(-5x\right)$

4. $-5\cos \left(x\right)$

Q. Thr period of the function : $f\left(x\right)=3\sin 2\left\{3x\right\}+5\cos 3\left\{2x\right\}$ is (where $\left\{\right\}$ denotes fraction part function)

Q. The graph of $f\left(x\right)=a\cos (bx+c)$ with $b>0$ is shown below. Then choose the correct option(s) for the given function?

1. Period of $f\left(x\right)$ is $\frac{2\pi }{3}$
2. $a=-1$
3. $b=3$
4. $a=1$

Q. The period of the function $f\left(x\right)=\sin |100x|$ is

1. $\frac{\pi }{50}$
2. $\frac{\pi }{100}$
3. $\frac{\pi }{25}$
4. Not defined

Q. If $\alpha ,\beta ,\gamma ,\delta$ are the smallest positive angles in ascending order of magnitude which have their sines equal to the positive quantity k, then the value of $4sin\frac{\alpha }{2}+3sin\frac{\beta }{2}+2sin\frac{\gamma }{2}+sin\frac{\delta }{2}$ is equal to

1. $2\sqrt{1-k}$
2. $\frac{1}{2}\sqrt{1+k}$
3. $2\sqrt{1+k}$
4. $Noneofthese$

Q. The fundamental period of $f\left(x\right)=\sin 2x$ is

1. $\frac{\pi }{2}$
2. $\pi$
3. $2\pi$
4. $4\pi$

Q. The graph of $f\left(x\right)=a\cos (bx+c)$ with $b>0$ is shown below. Then choose the correct option(s) for the given function?

1. Period of $f\left(x\right)$ is $\frac{2\pi }{3}$
2. $a=-1$
3. $b=3$
4. $a=1$

Q. If $f\left(x\right)=\sin \frac{x}{3}+\cos \frac{3x}{10}$ and $f(n\pi +x)=f\left(x\right),$ then the least positive integral value of $n$ is

Q. The number of solutions of the equation $(|\sin x|-1)(5|\sin x|-1)=0$ in $[0,2\pi ]$ is

1. $3$
2. $4$
3. $5$
4. $6$

Q.

$\frac{1+sin{600}^{\circ }-cos{600}^{\circ }}{1+sin{600}^{\circ }+cos{600}^{\circ }}$ = ?

1. $\frac{3-\sqrt{3}}{1-\sqrt{3}}$

2. -$\sqrt{3}$

3. $\sqrt{3}$

4. $\frac{\sqrt{3}-3}{1-\sqrt{3}}$