Question

What is cos theta when sin theta = sqrt 2/3

Answer 1

Answer:

Value of cosθ is ±√7/3 .

Step-by-step explanation:

According to the Question , value of :

$\red{\implies sin\theta = \dfrac{\sqrt2}{3}}$

And , we know the identity of sine and cosine as ,

$\boxed{\pink{\sf\implies sin^2\theta + cos^2\theta = 1} }$

Using , this identity we have ;

$\implies sin^2\theta + cos^2\theta = 1 \\\\\implies \bigg( \dfrac{\sqrt2}{3}\bigg)^2 + cos^2\theta = 1 \\\\\implies \dfrac{2}{9} + cos^2\theta = 1 \\\\\implies cos^2\theta = 1 - \dfrac{2}{9} \\\\\implies cos^2\theta = \dfrac{9-2}{9} \\\\\implies cos\theta = \sqrt{\dfrac{7}{9}} \\\\\underline{\boxed{\blue{\bf \implies cos\theta = \pm \dfrac{\sqrt 7 }{3}}}}$

Now , here since θ is in 2nd quadrant and in 2nd quadrant cos is negative . Hence ,the value of cos will be :

$\boxed{\orange{\bf \implies cos\theta =-\dfrac{\sqrt7}{3}}}$