Final answer:
To find the value of s in the interval (0, π/2) for tan s= 0.8855, use the inverse tangent function. For the condition cos s = -√2/2, use the inverse cosine function. And for the condition sin^2 s = 1/4, take the square root of both sides.
Step-by-step explanation:
To find the value of s in the interval (0, π/2) for tan s= 0.8855, you can use the inverse tangent function (also known as arctan) to find the angle. So, s = arctan(0.8855). Using a calculator, you can find that s ≈ 41.03°.
For the second question, to find the exact value of s in the interval (0, 2π) that satisfies the condition cos s = -√2/2, you can use the inverse cosine function (also known as arccos). So, s = arccos(-√2/2). Using a calculator, you can find that s = (5π/4) or 225°.
Lastly, for the condition sin^2 s = 1/4, you can take the square root of both sides to get sin s = ±1/2. Since the interval is (0, 2π), we can have two values for s: s = π/6 or 30°, and s = 5π/6 or 150°.