Why do we start measuring angle from positive direction of X axis only?

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Why do measure the angle from positive X axis in coordinate geometry? Further we also say clockwise rotation would produce negative angles? How can angles be negative? I mean, how much is $-30°$? Does that even make sense?




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    Why do measure the angle from positive X axis in coordinate geometry? Further we also say clockwise rotation would produce negative angles? How can angles be negative? I mean, how much is $-30°$? Does that even make sense?




    coordinate-systems




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      up vote
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      favorite









      up vote
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      down vote

      favorite











      Why do measure the angle from positive X axis in coordinate geometry? Further we also say clockwise rotation would produce negative angles? How can angles be negative? I mean, how much is $-30°$? Does that even make sense?




      coordinate-systems




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      Why do measure the angle from positive X axis in coordinate geometry? Further we also say clockwise rotation would produce negative angles? How can angles be negative? I mean, how much is $-30°$? Does that even make sense?





      coordinate-systems





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      asked 2 days ago









      William

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          There is no particular reason we measure positive angles as counterclockwise from the positive $x$ axis, it was adopted as a convention in order to standardize the way we do it. Negative angles are also used in the way you ask, as a clockwise rotation.






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            In the Argand diagram, $e^it$ is a point on the unit circle when $t$
            is real. It lies on the positive $x$-axis for $t=0$, and when $t$ increases
            it moves anti-clockwise about the unit circle, and when $t$ decreases
            it moves clockwise. This is the reason that in complex analysis, anti-clockwise is regarded as the positive direction.






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              Astronomy played a big part in the development of trigonometry and, in particular, angles. Consider a plane with the sun at the origin and the earth travelling, in the plane, in an almost circular path around the sun. Put your right hand on the origin with your thumb pointing north. Your fingers will curl in the direction that the earth is rotating and in the direction that the earth is travelling around the sun. This is called a right-handed system. Most, not all, of the sun-planet, planet-axis, and planet-moon systems in the solar system are right-handed systems. The bolts and lug nuts on most tires are right handed systems. Most bathroom faucet handles are right-handed systems. So it is convenient for counter clockwise to be the positive direction for an angle and for the counterclockwise direction to be the negative direction for an angle.






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                There is no particular reason we measure positive angles as counterclockwise from the positive $x$ axis, it was adopted as a convention in order to standardize the way we do it. Negative angles are also used in the way you ask, as a clockwise rotation.






                share|cite|improve this answer

























                  up vote
                  0
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                  There is no particular reason we measure positive angles as counterclockwise from the positive $x$ axis, it was adopted as a convention in order to standardize the way we do it. Negative angles are also used in the way you ask, as a clockwise rotation.






                  share|cite|improve this answer























                    up vote
                    0
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                    up vote
                    0
                    down vote









                    There is no particular reason we measure positive angles as counterclockwise from the positive $x$ axis, it was adopted as a convention in order to standardize the way we do it. Negative angles are also used in the way you ask, as a clockwise rotation.






                    share|cite|improve this answer













                    There is no particular reason we measure positive angles as counterclockwise from the positive $x$ axis, it was adopted as a convention in order to standardize the way we do it. Negative angles are also used in the way you ask, as a clockwise rotation.







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                    answered 2 days ago









                    Tyler6

                    430210




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                        In the Argand diagram, $e^it$ is a point on the unit circle when $t$
                        is real. It lies on the positive $x$-axis for $t=0$, and when $t$ increases
                        it moves anti-clockwise about the unit circle, and when $t$ decreases
                        it moves clockwise. This is the reason that in complex analysis, anti-clockwise is regarded as the positive direction.






                        share|cite|improve this answer

























                          up vote
                          0
                          down vote













                          In the Argand diagram, $e^it$ is a point on the unit circle when $t$
                          is real. It lies on the positive $x$-axis for $t=0$, and when $t$ increases
                          it moves anti-clockwise about the unit circle, and when $t$ decreases
                          it moves clockwise. This is the reason that in complex analysis, anti-clockwise is regarded as the positive direction.






                          share|cite|improve this answer























                            up vote
                            0
                            down vote










                            up vote
                            0
                            down vote









                            In the Argand diagram, $e^it$ is a point on the unit circle when $t$
                            is real. It lies on the positive $x$-axis for $t=0$, and when $t$ increases
                            it moves anti-clockwise about the unit circle, and when $t$ decreases
                            it moves clockwise. This is the reason that in complex analysis, anti-clockwise is regarded as the positive direction.






                            share|cite|improve this answer













                            In the Argand diagram, $e^it$ is a point on the unit circle when $t$
                            is real. It lies on the positive $x$-axis for $t=0$, and when $t$ increases
                            it moves anti-clockwise about the unit circle, and when $t$ decreases
                            it moves clockwise. This is the reason that in complex analysis, anti-clockwise is regarded as the positive direction.







                            share|cite|improve this answer













                            share|cite|improve this answer



                            share|cite|improve this answer











                            answered 2 days ago









                            Lord Shark the Unknown

                            83.9k949111




                            83.9k949111




















                                up vote
                                0
                                down vote













                                Astronomy played a big part in the development of trigonometry and, in particular, angles. Consider a plane with the sun at the origin and the earth travelling, in the plane, in an almost circular path around the sun. Put your right hand on the origin with your thumb pointing north. Your fingers will curl in the direction that the earth is rotating and in the direction that the earth is travelling around the sun. This is called a right-handed system. Most, not all, of the sun-planet, planet-axis, and planet-moon systems in the solar system are right-handed systems. The bolts and lug nuts on most tires are right handed systems. Most bathroom faucet handles are right-handed systems. So it is convenient for counter clockwise to be the positive direction for an angle and for the counterclockwise direction to be the negative direction for an angle.






                                share|cite|improve this answer

























                                  up vote
                                  0
                                  down vote













                                  Astronomy played a big part in the development of trigonometry and, in particular, angles. Consider a plane with the sun at the origin and the earth travelling, in the plane, in an almost circular path around the sun. Put your right hand on the origin with your thumb pointing north. Your fingers will curl in the direction that the earth is rotating and in the direction that the earth is travelling around the sun. This is called a right-handed system. Most, not all, of the sun-planet, planet-axis, and planet-moon systems in the solar system are right-handed systems. The bolts and lug nuts on most tires are right handed systems. Most bathroom faucet handles are right-handed systems. So it is convenient for counter clockwise to be the positive direction for an angle and for the counterclockwise direction to be the negative direction for an angle.






                                  share|cite|improve this answer























                                    up vote
                                    0
                                    down vote










                                    up vote
                                    0
                                    down vote









                                    Astronomy played a big part in the development of trigonometry and, in particular, angles. Consider a plane with the sun at the origin and the earth travelling, in the plane, in an almost circular path around the sun. Put your right hand on the origin with your thumb pointing north. Your fingers will curl in the direction that the earth is rotating and in the direction that the earth is travelling around the sun. This is called a right-handed system. Most, not all, of the sun-planet, planet-axis, and planet-moon systems in the solar system are right-handed systems. The bolts and lug nuts on most tires are right handed systems. Most bathroom faucet handles are right-handed systems. So it is convenient for counter clockwise to be the positive direction for an angle and for the counterclockwise direction to be the negative direction for an angle.






                                    share|cite|improve this answer













                                    Astronomy played a big part in the development of trigonometry and, in particular, angles. Consider a plane with the sun at the origin and the earth travelling, in the plane, in an almost circular path around the sun. Put your right hand on the origin with your thumb pointing north. Your fingers will curl in the direction that the earth is rotating and in the direction that the earth is travelling around the sun. This is called a right-handed system. Most, not all, of the sun-planet, planet-axis, and planet-moon systems in the solar system are right-handed systems. The bolts and lug nuts on most tires are right handed systems. Most bathroom faucet handles are right-handed systems. So it is convenient for counter clockwise to be the positive direction for an angle and for the counterclockwise direction to be the negative direction for an angle.







                                    share|cite|improve this answer













                                    share|cite|improve this answer



                                    share|cite|improve this answer











                                    answered 2 days ago









                                    steven gregory

                                    16.3k21955




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