Question

what is the measure of the reference angle for 142 degrees 40' 35" ?

Answer 1

what do they mean by a "reference"?

Answer 2

what's a reference angle?

Answer 3

the angle of less than 360 degrees that corresponds to an angle of over 360 degrees

Answer 4

well, a so-called reference angle is really the "cast shadow" of the angle you have

so \^142^o 40' 35" lands on the II quadrant, now if you were to say, have it CAST A SHADOW downward, that shaded section will be the reference angle

Answer 5

woops, missed something there :/

Answer 6

well, a so-called reference angle is really the "cast shadow" of the angle you have

so \(142^o 40' 35"\) lands on the II quadrant, now if you were to say, have it CAST A SHADOW downward, that shaded section will be the reference angle

Answer 7

oh okay, i sort of get it more now, thanks, but what do you mean about the shaded section being the reference angle?

Answer 8

so, the "ground where the shadow is being cast", is really the "x" axis
keep in mind that reference angles are per Quadrant

so this angle you have, is in the 2nd quadrant, so we're looking at \(142^o40'35" = 90 + 52^o40'35"\) so the "cast shadow" on the 2nd Quadrant, will be \(90- 52^o40'35"\)

Answer 9

so would that be the final answer?? :)

Answer 10

the answer will be \(90- 52^o40'35"\)

Answer 11

the 142 angle is taking up ALL 90 degrees of the 1 Quadrant, and eating up \(52^o40'35"\) of the 2nd Quadrant, so the reference angle is whatever the 2nd Quadrant has left after \(52^o40'35"\) has been "eaten up" from it

Answer 12

okay, well thank you sooooo muchhh!! :) i really appreciated your help!