Which of the following trigonometric values are negative? $\begin{aligned} & \text { I. } \sin…
Which of the following trigonometric values are negative?
$\begin{aligned} & \text { I. } \sin \left(-292^{\circ}\right) \\ & \text { II. } \tan \left(-190^{\circ}\right) \\ & \text { III. } \cos \left(-207^{\circ}\right) \\ & \text { IV. } \cot \left(-222^{\circ}\right)\end{aligned}$
II, III and IV
Only III
I and III
II and III
Solution
For option I,
$\sin \left(-292^{\circ}\right)=-\sin 292^{\circ}$
$\begin{aligned} & =-\sin \left(360^{\circ}-68^{\circ}\right)=-\sin 68^{\circ} \\ & =-(-)=+ \text { ve value }\end{aligned}$
So, clearly $\sin \left(-292^{\circ}\right)$ give + ve value.
For option II,
$\tan \left(-193^{\circ}\right)=-\tan 193^{\circ}$
$\begin{aligned} & =-\tan \left(180^{\circ}+13^{\circ}\right) \\ & =-\tan 13^{\circ}(- \text { ve value })\end{aligned}$
For option III ,
$\cos \left(-207^{\circ}\right)=\cos 207^{\circ}$
$\begin{aligned} & =\cos \left(180+27^{\circ}\right) \\ & =-\cos 27^{\circ} \text { (-ve value) }\end{aligned}$
For option IV,
$\cot \left(-222^{\circ}\right)=\cot \left(180^{\circ}+42^{\circ}\right)$
$=+\cot 42^{\circ}(+$ ve value $)$