Solution
- The number of possible outcomes in the sample space is simply gotten by multiplying out all the events together.
- There are 3 possible days: Tuesday, Wednesday, or Thursday. Thus, there are 3 possible outcomes.
- There are 3 possible times: 3PM, 4PM, or 5PM. Thus, there are 3 possible outcomes again.
- There are also 9 possible classrooms available meaning another 9 possible outcomes.
- Thus, the total possible outcomes in the sample space is
Answer: sqrt(2)/2 which is choice D
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Explanation
(3pi/4) radians converts to 135 degrees after multiplying by the conversion factor (180/pi).
The angle 135 degrees is in quadrant 2. We subtract the angle 135 from 180 to find the reference angle
180-135 = 45
Then you can use a 45-45-90 triangle to determine that the ratio of opposite over hypotenuse is sqrt(2)/2
sine is positive in quadrant 2
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Alternatively, you can use a unit circle. Refer to the diagram below. In red, I've circled the angle 3pi/4 radians. The terminal point for this angle has a y coordinate of sqrt(2)/2
Recall that y = sin(theta).
