Answer:

Explanation:
To find the value of cos 2θ given sin θ = 2/7 where 90° < θ < 180°, first use the trigonometric identity sin²θ + cos²θ = 1 to find cos θ:

Since 90° < θ < 180°, the cosine of θ is in quadrant II of the unit circle, and so cos θ is negative. Therefore:

Now we can use the cosine double angle identity to calculate cos 2θ.

Substitute the value of cos θ:

Therefore, when 90° < θ < 180° and sin θ = 2/7, the value of cos 2θ is 41/49.