Answer:
Value of cosθ is ±√7/3 .
Step-by-step explanation:
According to the Question , value of :
[tex]\red{\implies sin\theta = \dfrac{\sqrt2}{3}} [/tex]
And , we know the identity of sine and cosine as ,
[tex]\boxed{\pink{\sf\implies sin^2\theta + cos^2\theta = 1} }[/tex]
Using , this identity we have ;
[tex]\implies sin^2\theta + cos^2\theta = 1 \\\\\implies \bigg( \dfrac{\sqrt2}{3}\bigg)^2 + cos^2\theta = 1 \\\\\implies \dfrac{2}{9} + cos^2\theta = 1 \\\\\implies cos^2\theta = 1 - \dfrac{2}{9} \\\\\implies cos^2\theta = \dfrac{9-2}{9} \\\\\implies cos\theta = \sqrt{\dfrac{7}{9}} \\\\\underline{\boxed{\blue{\bf \implies cos\theta = \pm \dfrac{\sqrt 7 }{3}}}}[/tex]
Now , here since θ is in 2nd quadrant and in 2nd quadrant cos is negative . Hence ,the value of cos will be :
[tex]\boxed{\orange{\bf \implies cos\theta =-\dfrac{\sqrt7}{3}}}[/tex]
