A student is given that point P(a, b) lies on the terminal ray of angle Theta, which is between StartFraction 3 pi Over 2 EndFraction radians and 2Pi radians. The student uses the steps below to find cos Theta.

Step 1 Find the quadrant in which P(a, b) lies:
P(a, b) is in Quadrant IV.
Step 2 Use the point and the Pythagorean theorem to determine the value of r:
r = plus-or-minus StartRoot (a squared) + (b squared) EndRoot, but since r must be positive, r = StartRoot a squared + b squared EndRoot.
Step 3 Determine cos Theta.
cosine theta = StartFraction negative a Over StartRoot a squared + b squared EndRoot EndFraction = Negative StartFraction a StartRoot a squared + b squared EndRoot Over a squared + b squared EndRoot EndFraction, where a and b are positive.

Which of the following explains whether the student is correct?
The student made an error in step 3 because a is positive in Quadrant IV; therefore, cosine theta = StartFraction a Over StartRoot a squared + b squared EndRoot EndFraction = StartFraction a StartRoot a squared + b squared EndRoot Over a squared + b squared EndFraction.
The student made an error in step 3 because cosine theta = StartFraction negative b Over StartRoot a squared + b squared EndRoot EndFraction = Negative StartFraction b StartRoot a squared + b squared EndRoot Over a squared + b squared EndFraction.
The student made an error in step 2 because r is negative in Quadrant IV; therefore, r = Negative StartRoot a squared + b squared EndRoot.
The student made an error in step 2 because using the Pythagorean theorem gives r = plus-or-minus StartRoot (a squared) minus (b squared) EndRoot = StartRoot a squared minus b squared EndRoot.