Final answer:
To determine the radian measure of an angle in the second quadrant, we need to choose a value between π/2 and π radians, or 90° to 180°. Of the given options, Option b (17π/4) is the only angle that fits the criteria for the second quadrant. Therefore, the final answer is Option b (17π/4).
Step-by-step explanation:
The question is asking us to determine the radian measure of an angle in the second quadrant when given in standard position. To solve this, we need to recall that the second quadrant is where the angle measures greater than π/2 radians but less than π radians (90° to 180°).
Checking the given options, we're looking for a value that is equivalent to an angle measure between π/2 and π when reduced to its simplest form. Let's examine the options:
- Option a: 10π/3 - When reduced, it is greater than π, but 10π/3 falls into the fourth quadrant, not the second.
- Option b: 17π/4 - This can be simplified to 4π + π/4, which is between π and 2π, indicating it's in the second quadrant.
- Option c: 35π/6 - When reduced, it is greater than π, but 35π/6 falls into the first quadrant, not the second.
- Option d: 37π/8 - When simplified, it lies between 4π and π, indicating it could be in the second quadrant if not further reduced, but due to the denominator, it falls in the first quadrant.
So, the correct option for an angle in the second quadrant in standard position as a radian measure is Option b: 17π/4. Therefore, I choose Option b as the final answer.