a. The unit circle has equation
x² + y² = 1
Draw a line segment from the origin (0, 0) to any point (x, y) on the circle. θ ends in quadrant II, so that's where we'll find (x, y), with x < 0 and y > 0.
Note the resemblance to the Pythagorean identity,
cos²(θ) + sin²(θ) = 1
Let x = cos(θ) = -9/41. Solve for y :
(-9/41)² + y² = 1
81/1681 + y² = 1
y² = 1600/1681
y = +√(1600/1681)
y = 40/41
So the point on the circle has coordinates (-9/41, 40/41).
b. Since x = cos(θ), it follows that y = sin(θ) = 40/41.
c. By definition of tangent, tan(θ) = sin(θ)/cos(θ) = -40/9.