Reference Angles Given θ is in standard ... amazonaws com
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Reference Angles
Name _________________________________ Date ___________________ Period _______
Given ! is in standard position, the reference angle of !, noted !’, is the acute angle formed by the terminal side of ! and the horizontal x-axis. If ! lies in quadrant 1, then !’ = ! !
!’
Given ! is in standard position, the reference angle of !, noted !’, is the acute angle formed by the terminal side of ! and the horizontal x-axis. If ! lies in quadrant 2,
If ! lies in quadrant 1,
then !’ = 180° – ! or !’ = π – !
!
then !’ = !
!’
Given ! is in standard position, the reference angle of !, noted !’, is the acute angle formed by the terminal side of ! and the horizontal x-axis. If ! lies in quadrant 2,
If ! lies in quadrant 1,
then !’ = 180° – !
then !’ = !
or !’ = π – !
! !’
If ! lies in quadrant 3, then !’ = ! – 180° or !’ = ! – π
Given ! is in standard position, the reference angle of !, noted !’, is the acute angle formed by the terminal side of ! and the horizontal x-axis. If ! lies in quadrant 2,
If ! lies in quadrant 1,
then !’ = 180° – ! or !’ = π – !
then !’ = ! ! !’
If ! lies in quadrant 3,
If ! lies in quadrant 4,
then !’ = ! – 180°
then !’ = 360° – !
or !’ = ! – π
or !’ = 2π – ! © iTutoring.com Reference Angles Pg. 2
Given ! is in standard position, the reference angle of !, noted !’, is the acute angle formed by the terminal side of ! and the horizontal x-axis. Given ! = 45°
!
!’
Given ! is in standard position, the reference angle of !, noted !’, is the acute angle formed by the terminal side of ! and the horizontal x-axis. Given ! =
!
π 3
!’
© iTutoring.com Reference Angles Pg. 3
Given ! is in standard position, the reference angle of !, noted !’, is the acute angle formed by the terminal side of ! and the horizontal x-axis. Given ! = 160° ! !’
Given ! is in standard position, the reference angle of !, noted !’, is the acute angle formed by the terminal side of ! and the horizontal x-axis. 2π Given ! = 3 ! !’
© iTutoring.com Reference Angles Pg. 4
Given ! is in standard position, the reference angle of !, noted !’, is the acute angle formed by the terminal side of ! and the horizontal x-axis.
! !’ Given ! = 210°
Given ! is in standard position, the reference angle of !, noted !’, is the acute angle formed by the terminal side of ! and the horizontal x-axis.
!
Given ! =
5π 4
!’
© iTutoring.com Reference Angles Pg. 5
Given ! is in standard position, the reference angle of !, noted !’, is the acute angle formed by the terminal side of ! and the horizontal x-axis.
! !’ Given ! = 300°
Given ! is in standard position, the reference angle of !, noted !’, is the acute angle formed by the terminal side of ! and the horizontal x-axis.
! !’
Given ! =
11π 6
© iTutoring.com Reference Angles Pg. 6
Given ! is in standard position, the reference angle of !, noted !’, is the acute angle formed by the terminal side of ! and the horizontal x-axis.
coterminal ! 225° !’ Given ! = -135°
!
Given ! is in standard position, the reference angle of !, noted !’, is the acute angle formed by the terminal side of ! and the horizontal x-axis. Given ! = !
coterminal !
5π 3
π 3
!’
© iTutoring.com Reference Angles Pg. 7
Reference Angles
Name _________________________________ Date ___________________ Period _______
Given ! is in standard position, the reference angle of !, noted !’, is the acute angle formed by the terminal side of ! and the horizontal x-axis. If ! lies in quadrant 1, then !’ = ! !
!’
Given ! is in standard position, the reference angle of !, noted !’, is the acute angle formed by the terminal side of ! and the horizontal x-axis. If ! lies in quadrant 2,
If ! lies in quadrant 1,
then !’ = 180° – ! or !’ = π – !
!
then !’ = !
!’
Given ! is in standard position, the reference angle of !, noted !’, is the acute angle formed by the terminal side of ! and the horizontal x-axis. If ! lies in quadrant 2,
If ! lies in quadrant 1,
then !’ = 180° – !
then !’ = !
or !’ = π – !
! !’
If ! lies in quadrant 3, then !’ = ! – 180° or !’ = ! – π
Given ! is in standard position, the reference angle of !, noted !’, is the acute angle formed by the terminal side of ! and the horizontal x-axis. If ! lies in quadrant 2,
If ! lies in quadrant 1,
then !’ = 180° – ! or !’ = π – !
then !’ = ! ! !’
If ! lies in quadrant 3,
If ! lies in quadrant 4,
then !’ = ! – 180°
then !’ = 360° – !
or !’ = ! – π
or !’ = 2π – ! © iTutoring.com Reference Angles Pg. 2
Given ! is in standard position, the reference angle of !, noted !’, is the acute angle formed by the terminal side of ! and the horizontal x-axis. Given ! = 45°
!
!’
Given ! is in standard position, the reference angle of !, noted !’, is the acute angle formed by the terminal side of ! and the horizontal x-axis. Given ! =
!
π 3
!’
© iTutoring.com Reference Angles Pg. 3
Given ! is in standard position, the reference angle of !, noted !’, is the acute angle formed by the terminal side of ! and the horizontal x-axis. Given ! = 160° ! !’
Given ! is in standard position, the reference angle of !, noted !’, is the acute angle formed by the terminal side of ! and the horizontal x-axis. 2π Given ! = 3 ! !’
© iTutoring.com Reference Angles Pg. 4
Given ! is in standard position, the reference angle of !, noted !’, is the acute angle formed by the terminal side of ! and the horizontal x-axis.
! !’ Given ! = 210°
Given ! is in standard position, the reference angle of !, noted !’, is the acute angle formed by the terminal side of ! and the horizontal x-axis.
!
Given ! =
5π 4
!’
© iTutoring.com Reference Angles Pg. 5
Given ! is in standard position, the reference angle of !, noted !’, is the acute angle formed by the terminal side of ! and the horizontal x-axis.
! !’ Given ! = 300°
Given ! is in standard position, the reference angle of !, noted !’, is the acute angle formed by the terminal side of ! and the horizontal x-axis.
! !’
Given ! =
11π 6
© iTutoring.com Reference Angles Pg. 6
Given ! is in standard position, the reference angle of !, noted !’, is the acute angle formed by the terminal side of ! and the horizontal x-axis.
coterminal ! 225° !’ Given ! = -135°
!
Given ! is in standard position, the reference angle of !, noted !’, is the acute angle formed by the terminal side of ! and the horizontal x-axis. Given ! = !
coterminal !
5π 3
π 3
!’
© iTutoring.com Reference Angles Pg. 7
