Mary Jane Sterling is the author of Algebra I For Dummies and many other For Dummies titles. ����[/_�������qy��孧��qyXگ�;.+�\~������ Title: Drawing Angles in Standard Position Author: Tess Created Date: %PDF-1.3 Being able to recognize a particular angle by the quadrant its terminal side lies in and, conversely, to know which angles have their terminal sides in a particular quadrant is helpful when working in these areas. Angles measuring exactly 90, 180, 270, and 360 degrees do not have a terminal side that lies in a quadrant, and they’re referred to as quadrantal angles. Navigators, surveyors, and carpenters all use the same angle measures, but the angles start out in different positions or places. Angles in the standard position are used in calculus, geometry, trigonometry, and other math subjects as a basis for discussion. Trig functions of large and negative angles, Tangent function (tan) in right triangles, Cotangent function cot (in right triangles), Cosecant function csc (in right triangles), Finding slant distance along a slope or ramp. stream Recall than there are 2π radians in a full circle of 360°, An angle in standard position has its vertex at the origin of the coordinate plane. In the figure above, w… ��;�t���j_������+��k�k* The vertex an angle is drawn in what is called the "standard position". ���u�o�[���&��ed�y?�k4.t�T�k�#+�����kk� This measure can be written in a short form: If it is not ambiguous, we may use just a single letter to denote an angle. Angles in standard position that measure between 0 and 90 degrees have their terminal sides in Quadrant I. ���A���kWX�íۧqE�ĵ���i\ʝ�s��h�s~��� �}>���j+��3�*�Sd�9�q���}��7Q�PYA9m}�bȴwlV���υʦ��c���\�,��ڱ�JC�%*dա�zµ���cŷ*IW�:m˨,�T-m}ol T8"#�m���{>HȪ�[C��P�n�>e�{M�5�h TL����A�+��n�9*�P)FP����:�OkC�(� ������ʩ~��/���wk��t�q����('�J�����X}� One side of the angle is always fixed along the positive x-axis - that is, going to the right along the axis in the 3 o'clock direction (line BC). The measure of an angles can be expressed in degrees or radians, but in trigonometry radians are the most common. Only the position of the terminal ray determines the angle. Answers to Drawing Angles in Standard Position 1) x y 2) x y 3) x y 4) x y 5) x y 6) x y 7) x y 8) x y 9) x y 10) x y 11) x y 12) x y 13) x y 14) x y 15) x y 16) x y 17) x y 18) x y 19) x y 20) x y. In this position, the vertex of the angle (B) is on the origin of the x and y axis. the positive �P[�|c& �q'���D%7Y�Zc���d�+�V�Y���7ĝO|�;6��w'�7���U�� �(�⃗�FD��#1�Si5��-���SwBy��W��^y� u� �{.��-��x�� Tb��w-f-�F�t���&?e͒��*Pٯ�5Lv�'Y�F��Qv& +��L�@�0�H�~Ť�q�e��O����J���/�g}2��8����v�ꎜ�G��;[�*�ٺV�-u�. ��l���%�ƕ����H� .Wb����R��ee���xm]��ƅ�B�k�#+�������*Vp�r�z��%����Vp��,o}��4���h�u�u�tw������ Example #4: The point (9, -4) is on the terminal arm of an angle e. a) Sketch the angle in standard position and determine the measure of the reference angle. Ӹ�Ii��5ߖ:��ј~��a���[�ZN�rc� -�,[���(���7ZʮnH�^N���df��#�{�i]��}��k�T�Oԫ7���3E�ܐ�2�4�+���ŏ�G��t�e굆qΐ���H�c)�=�ږt}�kL��29F����B�Z�n�B�7ɖ�ʪJǇŵ��:���9�f���y��o�0��g߮�?`ͬ If the terminal ray moves clockwise instead of counterclockwise, then the measure is a negative value. x��\Y��~�_1�;�!����8����9�ֱ�w%KZ[q�Q��S����d$�|��B�N��)���ů��'�.r��k�哋A��/g���w��aܹ���)b��"��cvW����_��⃫��/�.�!���i�A� ���F���g�XaU�c7��s�B��ǡTf�x|=�pɀ�,xXV@�C1��p-�a�� ���z �#�� �`��p|ǀ�,���8�P��8bV�Ǿ�0Z��c��c��`�ڊ�)�8��1�#.ƃA��V���(��n�ci_0�X���8�B�~Ȁ# The angles measuring between 90 and 180 degrees have their terminal sides in Quadrant II. .Wާ8���'p������G1N� (at the 3 o'clock position as shown as BC above). If you have one angle of say 30°, another of 390°, the two terminal sides will be in the same place (390 = 360+30). In the figure above click 'reset' and drag the point A around counterclockwise. They would be in the same place on the plane but have different measures (30° and 390°). The amount we rotate it is called the measure of the angle and is measured in degrees or radians.This measure can be written in a short form: If it is not ambiguous, we may use just a single letter to denote an angle. For more on this see Coterminal angles. ��H�[7�Q&�[ �箧]?j�� sc䅝��-ёJ��D��ȕ��sl���z�BG��y�U��������hަ��I�� ���SG���w% '��q֥B��V8ΡvǦ��I/[�Ho�*KK�> ��:�B�'�s��� ����_L��V��Ö�5��'h0�-�y��o�Q���Í[���E�s�{~�_bv�-3�0�8@zl2�Qd>�m?��-l�c0SR���:Lک���i�����Aŵaz����*E7I�߽F��4 The side that is fixed along the positive x axis (BC) is called the initial side. .��7�F{��U�6V[w�O�RR� �sh�toOQV[��N�ϡ In trigonometry an angle is usually drawn in what is called the "standard position" as shown above. In trigonometry and most other mathematical disciplines, you draw angles in a standard, universal position, so that mathematicians around the world are drawing and talking about the same thing. *�Ǭʻ�%x���ݯ��ڔaCV��}%�m� ;'�G8�ꄂc�&�n,�T:����E�� �8�_����b�>}ƀ"j��d.R�t�>Cl���[e����4����������f�Q ���H��e ��$(�Bs{���|'��X���9P�n����B2O(�~��B ,r�p��q�p�`�Q&P%���<8����9�hE?�����r����S;���0F9�8���ʡ������M��p�JÎM�`��W)����! She has been teaching mathematics at Bradley University in Peoria, Illinois, for more than 30 years and has loved working with future business executives, physical therapists, teachers, and many others. %�쏢 In trigonometry an angle is usually drawn in what is called the "standard position" as shown below. ����a8�Z���]%p�ŷz̀#��ݏp��ngлN��t��^2��1�|�3�0?���W_1����t��u���8�\��'�s���p༲�8�v�!��z��8,t��K���8,���/��/�� ���sq!����r!����_3�{~À�-�g���GX��np���%���u�'��N��h=�?s���SVh�K��'(b��E�Cq� B��qT��0�r�N#�[N(2ԯ8@�D�u6!���bAv�}� YPȡc�42l� }A0,�8d2}��S�����-;�� of the angle is on the origin, Angles measuring between 180 and 270 have their terminal sides in Quadrant III, and those measuring between 270 and 360 have their terminal sides in Quadrant IV. To make the angle, imagine of a copy of this side being rotated about the origin to create the second side, called the terminal side. For example the letter θ (theta), Example #3: An angle is in standard position such that cosO= Sketch a diagram to show the two 13 possible values of O, to the nearest degree, if 00 < 3600 . <> See Trig functions of large and negative angles. �C9 q��` '�Nׁ\��b�cAF��;�귬9��HC8���p�������a6���ٗ(b�la8z���)0@�o�!�`���s���@�[T���Ă*�~Њ;� 4t(v�@��1`ؼ�tN��� :t��!�; See Radians and Degrees. In fact you can go around as many times as you like. Its initial ray (starting side) lies along the positive x-axis. x-axis Terminal side of an angle - trigonometry. These two angles would then be called coterminal angles.

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