Final answer
The value of cotθ, to the nearest hundredth, if cosθ = -0.68 and θ is in Quadrant II is approximately -0.94.
Explanation
The given identity, sinθ + cos²θ = 1, allows us to solve for sinθ using the information provided. As cosθ = -0.68 and θ is in Quadrant II, we can determine sinθ using the Pythagorean identity. Given that cosθ = -0.68, we first find sin²θ using sin²θ = 1 - cos²θ. Therefore, sin²θ = 1 - (-0.68)² = 1 - 0.4624 = 0.5376. Taking the square root of 0.5376 gives sinθ ≈ 0.7335. To find cotθ, we use the identities cotθ = cosθ / sinθ. Substituting the values, cotθ ≈ -0.68 / 0.7335 ≈ -0.94 when rounded to the nearest hundredth.
This process involves leveraging the given trigonometric identity to find the missing trigonometric ratio. First, determining sinθ using the Pythagorean identity with the known value of cosθ allows us to derive sinθ ≈ 0.7335. Then, applying the definition of cotangent as the ratio of cosine to sine yields cotθ ≈ -0.94 by substituting the given values. The solution is rounded to the nearest hundredth as requested.