Final answer:
To find the value of the missing variable, use the formula θ / t. In question a), w = 5π / 8 radians per second and t = 4 sec, θ = 5π / 4 radians. In question b), θ = 2π / 3 radians and t - 10 seconds.
Step-by-step explanation:
To find the value of the missing variable, we can use the formula θ / t. Let's start with question a) w = 5π / 8 radians per second and t = 4 sec. Plugging these values into the formula, we get θ / 4 = 5π / 8. To solve for θ, we can isolate it by multiplying both sides of the equation by 4, giving θ = (5π / 8) * 4 = 10π / 8 = 5π / 4 radians.
For question b) θ = 2π / 3 radians and t - 10 seconds. We can use the same formula θ / t and plug in the values to get (2π / 3) / (t - 10). We don't have enough information to solve for the value of t, so we can leave it as is.