Find the values of other five trigonometric functions if $\sin x=\frac{3}{5}, x$ lies in second quadrant.
$\sin x=\frac{3}{5}$
$\csc x=\frac{1}{\sin x}=\frac{1}{\left(\frac{3}{5}\right)}=\frac{5}{3}$
$\sin ^{2} x+\cos ^{2} x=1$
$\Rightarrow \cos ^{2} x=1-\sin ^{2} x$
$\Rightarrow \cos ^{2} x=1-\left(\frac{3}{5}\right)^{2}$
$\Rightarrow \cos ^{2} x=1-\frac{9}{25}$
$\Rightarrow \cos ^{2} x=\frac{16}{25}$
$\Rightarrow \cos x=\pm \frac{4}{5}$
since $x$ lies in the $2^{\text {nd }}$ quadrant, the value of $\cos x$ will be negative
$\therefore \cos x=-\frac{4}{5}$
$\sec x=\frac{1}{\cos x}=\frac{1}{\left(-\frac{4}{5}\right)}=-\frac{5}{4}$
$\tan x=\frac{\sin x}{\cos x}=\frac{\left(\frac{3}{5}\right)}{\left(-\frac{4}{5}\right)}=-\frac{3}{4}$
$\cot x=\frac{1}{\tan x}=-\frac{4}{3}$
The value of $\cot \frac{\pi}{24}$ is :
If $\left| {\,a\,{{\sin }^2}\theta + b\sin \theta \cos \theta + c\,{{\cos }^2}\theta - \frac{1}{2}(a + c)\,} \right|\, \le \frac{1}{2}k,$ then ${k^2}$ is equal to
If $\cot \,\theta + \tan \theta = m$ and $\sec \theta - \cos \theta = n,$ then which of the following is correct
Find the degree measures corresponding to the following radian measures (Use $\pi=\frac{22}{7}$ ).
$-4$
Find the radian measures corresponding to the following degree measures:
$240^{\circ}$