Answer:
[tex]\cos^{-1} (-\frac{\sqrt{2} }{2}) = 135^\circ[/tex]
Step-by-step explanation:
Let us assume that [tex]\theta = \cos^{-1} (-\frac{\sqrt{2} }{2})[/tex]
⇒ [tex]\cos \theta = -\frac{\sqrt{2} }{2} = - \frac{1}{\sqrt{2} }[/tex] ........... (1)
So, the [tex]\cos \theta[/tex] value is negative in the second and third quadrant and we know that [tex]\cos 45 = \frac{1}{\sqrt{2}}[/tex].
Therefore, [tex]\theta = \pi + \frac{\pi }{4}[/tex] or [tex]\theta = \pi - \frac{\pi }{4}[/tex]
And the general solution of equation (1) is given by
[tex]\theta = (2n + 1)\pi \pm \frac{\pi }{4}[/tex] for n = 0, 1, 2, ....
Since we need a definite solution of [tex]\theta[/tex] in the second quadrant, hence, [tex]\theta = \pi - \frac{\pi }{4} = 135^\circ[/tex]. (Answer)
