Answer : tanθ = sqrt(1 - (910)²) / 910
Given: that the terminal side of angle θ intersects the unit circle in the first quadrant at (910, y), we can find the value of tanθ using the coordinates.
Step-by-step explanation:
Recall that on the unit circle, tanθ = y/x. In this case, x = 910 and y is the unknown value. However, since we are in the first quadrant, both x and y will be positive.
To find y, we can use the Pythagorean theorem for the unit circle: x² + y² = 1.
Substitute x = 910:
(910)² + y² = 1
y² = 1 - (910)²
Now, since y is positive in the first quadrant, we take the positive square root:
y = sqrt(1 - (910)²)
Finally, find tanθ = y/x:
tanθ = sqrt(1 - (910)²) / 910