To find the values of cos(θ) and tan(θ) when sin(θ) = 3/7 and the angle's terminal point is located in Quadrant II, we can use the trigonometric identities. We can use the Pythagorean Identity to find cos(θ) and the tangent identity to find tan(θ). The values for cos(θ) and tan(θ) are -2√(10)/7 and 3√(10)/20 respectively.
To find the values of cos(θ) and tan(θ) when sin(θ) = 3/7 and the angle's terminal point is located in Quadrant II, we can use the trigonometric identities.
Since we know that sin(θ) = 3/7, we can use the Pythagorean Identity to find cos(θ). The Pythagorean Identity states that sin²(θ) + cos²(θ) = 1.
Substituting sin(θ) = 3/7 into the equation, we have (3/7)² + cos²(θ) = 1.
Simplifying, we get cos²(θ) = 1 - (3/7)^2 = 1 - 9/49 = 40/49.
Taking the square root of both sides, we find cos(θ) = ±√(40/49) = ±(2√(10)/7).
Since the angle's terminal point is located in Quadrant II, where cos(θ) < 0, we take the negative value, which gives us cos(θ) = -2√(10)/7.
To find tan(θ), we can use the tangent identity, which states that tan(θ) = sin(θ)/cos(θ).
Substituting the given values, we have tan(θ) = (3/7)/(-2√(10)/7) = -3/(-2√(10)) = 3√(10)/20.