Find the reference angle for each of the following.

Question

3.2 radians = _ radians

 5.42radians =_ radians

-1.7 radians=_  radians

sqrt2 radians=_  radians

Answer 1

3.2 radians is very close to pi radians. pi= about 3.14159 radians

which = 180 degrees, so 3.2 is slightly more than 180 degrees with the reference angle maybe a degree or so.

the reference angle is fairly small. = 3.2 - 3.14159 = 0.0584 radians

one radian = 180/pi = about 57.3 degrees

the reference angle for 3.2 radians = 0.0584 radians = .0584(180)/pi = .0584(57.3) = 3.35 degrees

2pi - 5.42 radians =

2(3.14159)- 5.42 radians = about 0.863 radians = .0863(57.3) = 49.45 degrees reference angle

-1.7 radians = 57.3(-1.7) = -97.41 degrees, that's in the 3rd quadrant, with reference angle = 180-97.41 = 82.59 degrees = about 1.44 radians

square root of 2 radians = about 1.414 radians which is in quadrant I. = about 81 degrees.

That is the reference angle sqr2 radians or 81 degrees. The angle itself is the reference angle