Question

find the exact value of sin 7pi/6 cos 7pi/6 and sin 4pi/3 cos 4pi/3 using the values of their respective trigonometric ratios in the first quadrant

Answer 1

Answer:

what do you mean by extract value

Answer 2

$\sin( \frac{7\pi}{6} ) = \sin(\pi - \frac{7\pi}{6} ) \\ \\ = \sin( \frac{6\pi - 7\pi}{6} ) \\ \\ = \sin( \frac{ - \pi}{ \: \: 6} ) \\ \\ = \sin( - 30°) \\ \\ = - \sin(30) \\ \\ = - \frac{1}{2}$

$\cos( \frac{7\pi}{6} ) = - \cos(\pi - \frac{7\pi}{6} ) \\ \\ = - \cos( \frac{ - \pi}{6} ) \\ \\ = - \cos(30°) \\ \\ = - \frac{ \sqrt{3} }{2}$

Similarly, other can be calculated.

I hope this helps you.