If $\cos x=-\frac{3}{5}, x$ lies in the third quadrant, find the values of other five trigonometric functions.
since $\cos x=-\frac{3}{5},$ we have sec $x=-\frac{5}{3}$
Now $\sin ^{2} x+\cos ^{2} x=1, \text { i.e., } \sin ^{2} x=1-\cos ^{2} x $
or $\sin ^{2} x=1-\frac{9}{25}=\frac{16}{25}$
Hence $\quad \sin x=\pm \frac{4}{5}$
since $x$ lies in third quadrant, $\sin x$ is negative. Therefore
$\sin x=-\frac{4}{5}$
which also gives
${\cos ec}\, x=-\frac{5}{4}$
Further, we have
$\tan x=\frac{\sin x}{\cos x}=\frac{4}{3} \text { and } \cot x=\frac{\cos x}{\sin x}=\frac{3}{4}$
Find the degree measures corresponding to the following radian measures ( Use $\pi=\frac{22}{7}$ ).
$\frac{7 \pi}{6}$
If $sin\theta_1 + sin\theta_2 + sin\theta_3 = 3,$ then $cos\theta_1 + cos\theta_2 + cos\theta_3=$
The value of $6({\sin ^6}\theta + {\cos ^6}\theta ) - 9({\sin ^4}\theta + {\cos ^4}\theta ) + 4$ is
At what time between $10\,\,O'clock$ and $11\,\,O 'clock$ are the two hands of a clock symmetric with respect to the vertical line (give the answer to the nearest second)?
Find, $\sin \frac{x}{2}, \cos \frac{x}{2}$ and $\tan \frac{x}{2}$ for $\cos x=-\frac{1}{3}, x$ in quadrant $III.$