Final answer:
To verify if theta is within a specific interval, compare it to the lower and upper bounds of the interval, ensuring theta is expressed in the same units. Theta is within the interval if it's greater than or equal to the lower bound and less than or equal to the upper bound.
Step-by-step explanation:
To determine if an angle, denoted here as theta (θ), is within a given interval, you would typically compare its value to the endpoints of the interval. Intervals are usually given in degrees for angles measured in degrees, or in radians for angles measured in radians. Here's a step-by-step approach on how to check if theta is in an interval:
- Ensure that theta is in the same unit (degrees or radians) as the interval's endpoints.
- Compare theta to the lower bound of the interval. If theta is larger than or equal to the lower bound, then it may be in the interval.
- Compare theta to the upper bound of the interval. If theta is smaller than or equal to the upper bound, then it is within the interval.
- If both step 2 and step 3 are true, then theta is within the interval. If either is false, it is not in the interval.
For example, to check if theta is in the interval [45°, 90°], you'd first verify that theta is in degrees. If theta were 60°, since 60° >= 45° and 60° <= 90°, we conclude that it is within the interval.