Answer: cosθ + sinθ = -1/4.
Step-by-step explanation:
cos theta + sin theta = -√(3^2 - 4^2) / 4 = -1/4
The given equation is tanθ = -3/4. We can use the Pythagorean identity to find cosθ and sinθ, which states that cos²θ + sin²θ = 1.
Since we know that tanθ = -3/4, we can substitute this value into the Pythagorean identity to get:
cos²θ + (-3/4)² = 1
Solving for cosθ gives us cosθ = √(3² - 4²) / 4 = -1/4.
Similarly, we can solve for sinθ to get sinθ = -3/4.
Now, we can add cosθ and sinθ together to get cosθ + sinθ = -1/4.