which could be the measure of an angle where sin= rad2/2

Question

∏=pi

option1. 7∏/4

option2. 2∏/3

option3. 3∏/4

Answer 1

2/2=1; a radian is 180/pi°=57.29577951.....°

6.28....pi=360°

asin(57.29)=1.57rad, and -4.74rad

Answer 2

The answer is option 3. Sin(x) = rad2/2 is our given equation. We know sine is positive in the 1st and 2nd quadrants. We also know that we need a 45 degree relative to the x-axis to get a value of sine that is equal to rad2/2 (reference the unit circle to confirm this). The only answer that gives a relative angle of 45 degrees and is in the 1st or second quadrant is option 3. 3pi/4 = 135 degrees (again look at a unit circle to understand this visually). I hope this helps!