If $\cot x=-\frac{5}{12}, x$ lies in second quadrant, find the values of other five trigonometric functions.
since $\cot x=-\frac{5}{12},$ we have $\tan x=-\frac{12}{5}$
Now $\sec ^{2} x=1+\tan ^{2} x=1+\frac{144}{25}=\frac{169}{25}$
Hence $\sec x=\pm \frac{13}{5}$
since $x$ lies in second quadrant, sec $x$ will be negative. Therefore
$\sec x=-\frac{13}{5}$
which also gives
$\cos x=-\frac{5}{13}$
Further, we have
$\sin x =\tan x \cos x=\left(-\frac{12}{5}\right) \times\left(-\frac{5}{13}\right)=\frac{12}{13} $
and $\cos ec\, x =\frac{1}{\sin x}=\frac{13}{12}$
Find the value of:
$\sin 75^{\circ}$
If $\sin x = \frac{{ - 24}}{{25}},$ then the value of $\tan \, x$ is
Find the radian measures corresponding to the following degree measures:
$240^{\circ}$
Find the degree measures corresponding to the following radian measures (Use $\pi=\frac{22}{7}$ ).
$\frac{11}{16}$
If $x + \frac{1}{x} = 2\cos \alpha $, then ${x^n} + \frac{1}{{{x^n}}} = $