Solve both parts and justify the conditions used. Part A: For π<α<3π/2 and cos α=−3/5, determine the sign and value of sin(α/2). Part B: Evaluate without a calculator.

1. Part A reasoning

2. Select an identity that matches the structure, retain signs and check denominators.

3. Calculate or simplify this relation.

   $$\pi/2<\alpha/2<3\pi/4;\quad\sin(\alpha/2)=\sqrt{4/5}$$

4. The interval, not merely the terminal-ray quadrant, fixes the half-angle sign; adding 2π to α reverses that sign.

5. Part B reasoning

6. Use unit-circle symmetry and periodicity; determine the sign before simplifying.

7. Calculate or simplify this relation.

   $$\sin(\pi)+\sin(0)=0$$

8. The sine coordinate is zero at integer multiples of π.

A: Positive, equal to 2/√5. B: The requested value is 0.

Checks and common pitfalls: The interval, not merely the terminal-ray quadrant, fixes the half-angle sign; adding 2π to α reverses that sign. The sine coordinate is zero at integer multiples of π.