Final answer:
To find the value of sin θ when cos θ = 4√41 and θ is in quadrant 4, we can use the Pythagorean identity and solve for sin θ. sin θ = √655.
Step-by-step explanation:
To find the value of sin θ, we can use the Pythagorean identity: sin^2θ + cos^2θ = 1. Since we know that cos θ = 4√41, we can substitute this value into the equation and solve for sin θ.
First, square both sides of the equation: (cos θ)^2 = (4√41)^2 = 16*41 = 656.
Then, subtract the squared value of cos θ from both sides: sin^2θ = 1 - 656 = -655.
Finally, take the square root of both sides to find the value of sin θ: sin θ = ±√-655. Since θ is in quadrant 4, sin θ will be positive. So, sin θ = √655.