Rectangle and Trigonometric Functions
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This example demonstrates the relationship between a rectangle and trigonometric functions. Key mathematical concepts include the properties of a rectangle and sine and cosine functions. Using GeoGebra commands such as Intersect, Point, Segment, etc., a rectangle is constructed and its relationship with trigonometric functions is observed. Suitable for high school mathematics education.
GeoGebra Commands & Parameters
Intersect(xAxis, yAxis) → APoint(xAxis) → BPoint(yAxis) → CSegment(A, B) → aSegment(A, C) → bPoint(a) → DPoint(b) → EOrthogonalLine(D, a) → cOrthogonalLine(E, b) → dIntersect(c, d) → FSegment(E, F) → eSegment(F, D) → fSegment(E, A) → gSegment(A, D) → hCircle(G, n) → kPoint(k) → HSegment(G, H) → jCircle(G, i) → pOrthogonalLine(G, j) → lIntersect(p, l, 2) → IOrthogonalLine(I, j) → mOrthogonalLine(I, m) → qOrthogonalLine(H, j) → rIntersect(q, r) → JSegment(I, G) → sSegment(I, J) → tSegment(J, H) → a_1Polygon(I, G, H, J) → poly1, i_1, g_1, h_1, j_1Circle(G_1, n) → k_1Point(k_1) → H_1Segment(G_1, H_1) → j_2Circle(G_1, i) → p_1OrthogonalLine(G_1, j_2) → l_1Intersect(p_1, l_1, 2) → I_1OrthogonalLine(I_1, j_2) → m_1OrthogonalLine(I_1, m_1) → q_1OrthogonalLine(H_1, j_2) → r_1Intersect(q_1, r_1) → J_1Segment(I_1, G_1) → s_1Segment(I_1, J_1) → t_1Segment(J_1, H_1) → a_2Polygon(I_1, G_1, H_1, J_1) → poly1_1, i_2, g_2, h_2, j_3Circle(G_2, n) → k_2Point(k_2) → H_2Segment(G_2, H_2) → j_4Circle(G_2, i) → p_2OrthogonalLine(G_2, j_4) → l_2Intersect(p_2, l_2, 2) → I_2OrthogonalLine(I_2, j_4) → m_2OrthogonalLine(I_2, m_2) → q_2OrthogonalLine(H_2, j_4) → r_2Intersect(q_2, r_2) → J_2Segment(I_2, G_2) → s_2Segment(I_2, J_2) → t_2Segment(J_2, H_2) → a_3Polygon(I_2, G_2, H_2, J_2) → poly1_2, i_3, g_3, h_3, j_5Circle(G_3, n) → k_3Point(k_3) → H_3Segment(G_3, H_3) → j_6Circle(G_3, i) → p_3OrthogonalLine(G_3, j_6) → l_3Intersect(p_3, l_3, 2) → I_3OrthogonalLine(I_3, j_6) → m_3OrthogonalLine(I_3, m_3) → q_3OrthogonalLine(H_3, j_6) → r_3Intersect(q_3, r_3) → J_3Segment(I_3, G_3) → s_3Segment(I_3, J_3) → t_3Segment(J_3, H_3) → a_4Polygon(I_3, G_3, H_3, J_3) → poly1_3, i_4, g_4, h_4, j_7Circle(G_4, n) → k_4Point(k_4) → H_4Segment(G_4, H_4) → j_8Circle(G_4, i) → p_4OrthogonalLine(G_4, j_8) → l_4Intersect(p_4, l_4, 2) → I_4OrthogonalLine(I_4, j_8) → m_4OrthogonalLine(I_4, m_4) → q_4OrthogonalLine(H_4, j_8) → r_4Intersect(q_4, r_4) → J_4Segment(I_4, G_4) → s_4Segment(I_4, J_4) → t_4Segment(J_4, H_4) → a_5Polygon(I_4, G_4, H_4, J_4) → poly1_4, i_5, g_5, h_5, j_9Circle(G_5, n) → k_5Point(k_5) → H_5Segment(G_5, H_5) → j_{10}Circle(G_5, i) → p_5OrthogonalLine(G_5, j_{10}) → l_5Intersect(p_5, l_5, 2) → I_5OrthogonalLine(I_5, j_{10}) → m_5OrthogonalLine(I_5, m_5) → q_5OrthogonalLine(H_5, j_{10}) → r_5Intersect(q_5, r_5) → J_5Segment(I_5, G_5) → s_5Segment(I_5, J_5) → t_5Segment(J_5, H_5) → a_6Polygon(I_5, G_5, H_5, J_5) → poly1_5, i_6, g_6, h_6, j_{11}Circle(G_6, n) → k_6Point(k_6) → H_6Segment(G_6, H_6) → j_{12}Circle(G_6, i) → p_6OrthogonalLine(G_6, j_{12}) → l_6Intersect(p_6, l_6, 2) → I_6OrthogonalLine(I_6, j_{12}) → m_6OrthogonalLine(I_6, m_6) → q_6OrthogonalLine(H_6, j_{12}) → r_6Intersect(q_6, r_6) → J_6Segment(I_6, G_6) → s_6Segment(I_6, J_6) → t_6Segment(J_6, H_6) → a_7Polygon(I_6, G_6, H_6, J_6) → poly1_6, i_7, g_7, h_7, j_{13}Circle(G_7, n) → k_7Point(k_7) → H_7Segment(G_7, H_7) → j_{14}Circle(G_7, i) → p_7OrthogonalLine(G_7, j_{14}) → l_7Intersect(p_7, l_7, 2) → I_7OrthogonalLine(I_7, j_{14}) → m_7OrthogonalLine(I_7, m_7) → q_7OrthogonalLine(H_7, j_{14}) → r_7Intersect(q_7, r_7) → J_7Segment(I_7, G_7) → s_7Segment(I_7, J_7) → t_7Segment(J_7, H_7) → a_8Polygon(I_7, G_7, H_7, J_7) → poly1_7, i_8, g_8, h_8, j_{15}Circle(G_8, n) → k_8Point(k_8) → H_8Segment(G_8, H_8) → j_{16}Circle(G_8, i) → p_8OrthogonalLine(G_8, j_{16}) → l_8Intersect(p_8, l_8, 2) → I_8OrthogonalLine(I_8, j_{16}) → m_8OrthogonalLine(I_8, m_8) → q_8OrthogonalLine(H_8, j_{16}) → r_8Intersect(q_8, r_8) → J_8Segment(I_8, G_8) → s_8Segment(I_8, J_8) → t_8Segment(J_8, H_8) → a_9Polygon(I_8, G_8, H_8, J_8) → poly1_8, i_9, g_9, h_9, j_{17}Circle(G_9, n) → k_9Point(k_9) → H_9Segment(G_9, H_9) → j_{18}Circle(G_9, i) → p_9OrthogonalLine(G_9, j_{18}) → l_9Intersect(p_9, l_9, 2) → I_9OrthogonalLine(I_9, j_{18}) → m_9OrthogonalLine(I_9, m_9) → q_9OrthogonalLine(H_9, j_{18}) → r_9Intersect(q_9, r_9) → J_9Segment(I_9, G_9) → s_9Segment(I_9, J_9) → t_9Segment(J_9, H_9) → a_{10}Polygon(I_9, G_9, H_9, J_9) → poly1_9, i_{10}, g_{10}, h_{10}, j_{19}Circle(G_{10}, n) → k_{10}Point(k_{10}) → H_{10}Segment(G_{10}, H_{10}) → j_{20}Circle(G_{10}, i) → p_{10}OrthogonalLine(G_{10}, j_{20}) → l_{10}Intersect(p_{10}, l_{10}, 2) → I_{10}OrthogonalLine(I_{10}, j_{20}) → m_{10}OrthogonalLine(I_{10}, m_{10}) → q_{10}OrthogonalLine(H_{10}, j_{20}) → r_{10}Intersect(q_{10}, r_{10}) → J_{10}Segment(I_{10}, G_{10}) → s_{10}Segment(I_{10}, J_{10}) → t_{10}Segment(J_{10}, H_{10}) → a_{11}Polygon(I_{10}, G_{10}, H_{10}, J_{10}) → poly1_{10}, i_{11}, g_{11}, h_{11}, j_{21}Circle(G_{11}, n) → k_{11}Point(k_{11}) → H_{11}Segment(G_{11}, H_{11}) → j_{22}Circle(G_{11}, i) → p_{11}OrthogonalLine(G_{11}, j_{22}) → l_{11}Intersect(p_{11}, l_{11}, 2) → I_{11}OrthogonalLine(I_{11}, j_{22}) → m_{11}OrthogonalLine(I_{11}, m_{11}) → q_{11}OrthogonalLine(H_{11}, j_{22}) → r_{11}Intersect(q_{11}, r_{11}) → J_{11}Segment(I_{11}, G_{11}) → s_{11}Segment(I_{11}, J_{11}) → t_{11}Segment(J_{11}, H_{11}) → a_{12}Polygon(I_{11}, G_{11}, H_{11}, J_{11}) → poly1_{11}, i_{12}, g_{12}, h_{12}, j_{23}Circle(G_{12}, n) → k_{12}Point(k_{12}) → H_{12}Segment(G_{12}, H_{12}) → j_{24}Circle(G_{12}, i) → p_{12}OrthogonalLine(G_{12}, j_{24}) → l_{12}Intersect(p_{12}, l_{12}, 2) → I_{12}OrthogonalLine(I_{12}, j_{24}) → m_{12}OrthogonalLine(I_{12}, m_{12}) → q_{12}OrthogonalLine(H_{12}, j_{24}) → r_{12}Intersect(q_{12}, r_{12}) → J_{12}Segment(I_{12}, G_{12}) → s_{12}Segment(I_{12}, J_{12}) → t_{12}Segment(J_{12}, H_{12}) → a_{13}Polygon(I_{12}, G_{12}, H_{12}, J_{12}) → poly1_{12}, i_{13}, g_{13}, h_{13}, j_{25}Circle(G_{13}, n) → k_{13}Point(k_{13}) → H_{13}Segment(G_{13}, H_{13}) → j_{26}Circle(G_{13}, i) → p_{13}OrthogonalLine(G_{13}, j_{26}) → l_{13}Intersect(p_{13}, l_{13}, 2) → I_{13}OrthogonalLine(I_{13}, j_{26}) → m_{13}OrthogonalLine(I_{13}, m_{13}) → q_{13}OrthogonalLine(H_{13}, j_{26}) → r_{13}Intersect(q_{13}, r_{13}) → J_{13}Segment(I_{13}, G_{13}) → s_{13}Segment(I_{13}, J_{13}) → t_{13}Segment(J_{13}, H_{13}) → a_{14}Polygon(I_{13}, G_{13}, H_{13}, J_{13}) → poly1_{13}, i_{14}, g_{14}, h_{14}, j_{27}Circle(G_{14}, n) → k_{14}Point(k_{14}) → H_{14}Segment(G_{14}, H_{14}) → j_{28}Circle(G_{14}, i) → p_{14}OrthogonalLine(G_{14}, j_{28}) → l_{14}Intersect(p_{14}, l_{14}, 2) → I_{14}OrthogonalLine(I_{14}, j_{28}) → m_{14}OrthogonalLine(I_{14}, m_{14}) → q_{14}OrthogonalLine(H_{14}, j_{28}) → r_{14}Intersect(q_{14}, r_{14}) → J_{14}Segment(I_{14}, G_{14}) → s_{14}Segment(I_{14}, J_{14}) → t_{14}Segment(J_{14}, H_{14}) → a_{15}Polygon(I_{14}, G_{14}, H_{14}, J_{14}) → poly1_{14}, i_{15}, g_{15}, h_{15}, j_{29}Circle(G_{15}, n) → k_{15}Point(k_{15}) → H_{15}Segment(G_{15}, H_{15}) → j_{30}Circle(G_{15}, i) → p_{15}OrthogonalLine(G_{15}, j_{30}) → l_{15}Intersect(p_{15}, l_{15}, 2) → I_{15}OrthogonalLine(I_{15}, j_{30}) → m_{15}OrthogonalLine(I_{15}, m_{15}) → q_{15}OrthogonalLine(H_{15}, j_{30}) → r_{15}Intersect(q_{15}, r_{15}) → J_{15}Segment(I_{15}, G_{15}) → s_{15}Segment(I_{15}, J_{15}) → t_{15}Segment(J_{15}, H_{15}) → a_{16}Polygon(I_{15}, G_{15}, H_{15}, J_{15}) → poly1_{15}, i_{16}, g_{16}, h_{16}, j_{31}Circle(G_{16}, n) → k_{16}Point(k_{16}) → H_{16}Segment(G_{16}, H_{16}) → j_{32}Circle(G_{16}, i) → p_{16}OrthogonalLine(G_{16}, j_{32}) → l_{16}Intersect(p_{16}, l_{16}, 2) → I_{16}OrthogonalLine(I_{16}, j_{32}) → m_{16}OrthogonalLine(I_{16}, m_{16}) → q_{16}OrthogonalLine(H_{16}, j_{32}) → r_{16}Intersect(q_{16}, r_{16}) → J_{16}Segment(I_{16}, G_{16}) → s_{16}Segment(I_{16}, J_{16}) → t_{16}Segment(J_{16}, H_{16}) → a_{17}Polygon(I_{16}, G_{16}, H_{16}, J_{16}) → poly1_{16}, i_{17}, g_{17}, h_{17}, j_{33}Circle(G_{17}, n) → k_{17}Point(k_{17}) → H_{17}Segment(G_{17}, H_{17}) → j_{34}Circle(G_{17}, i) → p_{17}OrthogonalLine(G_{17}, j_{34}) → l_{17}Intersect(p_{17}, l_{17}, 2) → I_{17}OrthogonalLine(I_{17}, j_{34}) → m_{17}OrthogonalLine(I_{17}, m_{17}) → q_{17}OrthogonalLine(H_{17}, j_{34}) → r_{17}Intersect(q_{17}, r_{17}) → J_{17}Segment(I_{17}, G_{17}) → s_{17}Segment(I_{17}, J_{17}) → t_{17}Segment(J_{17}, H_{17}) → a_{18}Polygon(I_{17}, G_{17}, H_{17}, J_{17}) → poly1_{17}, i_{18}, g_{18}, h_{18}, j_{35}Circle(G_{18}, n) → k_{18}Point(k_{18}) → H_{18}Segment(G_{18}, H_{18}) → j_{36}Circle(G_{18}, i) → p_{18}OrthogonalLine(G_{18}, j_{36}) → l_{18}Intersect(p_{18}, l_{18}, 2) → I_{18}OrthogonalLine(I_{18}, j_{36}) → m_{18}OrthogonalLine(I_{18}, m_{18}) → q_{18}OrthogonalLine(H_{18}, j_{36}) → r_{18}Intersect(q_{18}, r_{18}) → J_{18}Segment(I_{18}, G_{18}) → s_{18}Segment(I_{18}, J_{18}) → t_{18}Segment(J_{18}, H_{18}) → a_{19}Polygon(I_{18}, G_{18}, H_{18}, J_{18}) → poly1_{18}, i_{19}, g_{19}, h_{19}, j_{37}Circle(G_{19}, n) → k_{19}Point(k_{19}) → H_{19}Segment(G_{19}, H_{19}) → j_{38}Circle(G_{19}, i) → p_{19}OrthogonalLine(G_{19}, j_{38}) → l_{19}Intersect(p_{19}, l_{19}, 2) → I_{19}OrthogonalLine(I_{19}, j_{38}) → m_{19}OrthogonalLine(I_{19}, m_{19}) → q_{19}OrthogonalLine(H_{19}, j_{38}) → r_{19}Intersect(q_{19}, r_{19}) → J_{19}Segment(I_{19}, G_{19}) → s_{19}Segment(I_{19}, J_{19}) → t_{19}Segment(J_{19}, H_{19}) → a_{20}Polygon(I_{19}, G_{19}, H_{19}, J_{19}) → poly1_{19}, i_{20}, g_{20}, h_{20}, j_{39}Circle(G_{20}, n) → k_{20}Point(k_{20}) → H_{20}Segment(G_{20}, H_{20}) → j_{40}Circle(G_{20}, i) → p_{20}OrthogonalLine(G_{20}, j_{40}) → l_{20}Intersect(p_{20}, l_{20}, 2) → I_{20}OrthogonalLine(I_{20}, j_{40}) → m_{20}OrthogonalLine(I_{20}, m_{20}) → q_{20}OrthogonalLine(H_{20}, j_{40}) → r_{20}Intersect(q_{20}, r_{20}) → J_{20}Segment(I_{20}, G_{20}) → s_{20}Segment(I_{20}, J_{20}) → t_{20}Segment(J_{20}, H_{20}) → a_{21}Polygon(I_{20}, G_{20}, H_{20}, J_{20}) → poly1_{20}, i_{21}, g_{21}, h_{21}, j_{41}Circle(G_{21}, n) → k_{21}Point(k_{21}) → H_{21}Segment(G_{21}, H_{21}) → j_{42}Circle(G_{21}, i) → p_{21}OrthogonalLine(G_{21}, j_{42}) → l_{21}Intersect(p_{21}, l_{21}, 2) → I_{21}OrthogonalLine(I_{21}, j_{42}) → m_{21}OrthogonalLine(I_{21}, m_{21}) → q_{21}OrthogonalLine(H_{21}, j_{42}) → r_{21}Intersect(q_{21}, r_{21}) → J_{21}Segment(I_{21}, G_{21}) → s_{21}Segment(I_{21}, J_{21}) → t_{21}Segment(J_{21}, H_{21}) → a_{22}Polygon(I_{21}, G_{21}, H_{21}, J_{21}) → poly1_{21}, i_{22}, g_{22}, h_{22}, j_{43}Circle(G_{22}, n) → k_{22}Point(k_{22}) → H_{22}Segment(G_{22}, H_{22}) → j_{44}Circle(G_{22}, i) → p_{22}OrthogonalLine(G_{22}, j_{44}) → l_{22}Intersect(p_{22}, l_{22}, 2) → I_{22}OrthogonalLine(I_{22}, j_{44}) → m_{22}OrthogonalLine(I_{22}, m_{22}) → q_{22}OrthogonalLine(H_{22}, j_{44}) → r_{22}Intersect(q_{22}, r_{22}) → J_{22}Segment(I_{22}, G_{22}) → s_{22}Segment(I_{22}, J_{22}) → t_{22}Segment(J_{22}, H_{22}) → a_{23}Polygon(I_{22}, G_{22}, H_{22}, J_{22}) → poly1_{22}, i_{23}, g_{23}, h_{23}, j_{45}Circle(G_{23}, n) → k_{23}Point(k_{23}) → H_{23}Segment(G_{23}, H_{23}) → j_{46}Circle(G_{23}, i) → p_{23}OrthogonalLine(G_{23}, j_{46}) → l_{23}Intersect(p_{23}, l_{23}, 2) → I_{23}OrthogonalLine(I_{23}, j_{46}) → m_{23}OrthogonalLine(I_{23}, m_{23}) → q_{23}OrthogonalLine(H_{23}, j_{46}) → r_{23}Intersect(q_{23}, r_{23}) → J_{23}Segment(I_{23}, G_{23}) → s_{23}Segment(I_{23}, J_{23}) → t_{23}Segment(J_{23}, H_{23}) → a_{24}Polygon(I_{23}, G_{23}, H_{23}, J_{23}) → poly1_{23}, i_{24}, g_{24}, h_{24}, j_{47}Circle(G_{24}, n) → k_{24}Point(k_{24}) → H_{24}Segment(G_{24}, H_{24}) → j_{48}Circle(G_{24}, i) → p_{24}OrthogonalLine(G_{24}, j_{48}) → l_{24}Intersect(p_{24}, l_{24}, 2) → I_{24}OrthogonalLine(I_{24}, j_{48}) → m_{24}OrthogonalLine(I_{24}, m_{24}) → q_{24}OrthogonalLine(H_{24}, j_{48}) → r_{24}Intersect(q_{24}, r_{24}) → J_{24}Segment(I_{24}, G_{24}) → s_{24}Segment(I_{24}, J_{24}) → t_{24}Segment(J_{24}, H_{24}) → a_{25}Polygon(I_{24}, G_{24}, H_{24}, J_{24}) → poly1_{24}, i_{25}, g_{25}, h_{25}, j_{49}Circle(G_{25}, n) → k_{25}Point(k_{25}) → H_{25}Segment(G_{25}, H_{25}) → j_{50}Circle(G_{25}, i) → p_{25}OrthogonalLine(G_{25}, j_{50}) → l_{25}Intersect(p_{25}, l_{25}, 2) → I_{25}OrthogonalLine(I_{25}, j_{50}) → m_{25}OrthogonalLine(I_{25}, m_{25}) → q_{25}OrthogonalLine(H_{25}, j_{50}) → r_{25}Intersect(q_{25}, r_{25}) → J_{25}Segment(I_{25}, G_{25}) → s_{25}Segment(I_{25}, J_{25}) → t_{25}Segment(J_{25}, H_{25}) → a_{26}Polygon(I_{25}, G_{25}, H_{25}, J_{25}) → poly1_{25}, i_{26}, g_{26}, h_{26}, j_{51}Circle(G_{26}, n) → k_{26}Point(k_{26}) → H_{26}Segment(G_{26}, H_{26}) → j_{52}Circle(G_{26}, i) → p_{26}OrthogonalLine(G_{26}, j_{52}) → l_{26}Intersect(p_{26}, l_{26}, 2) → I_{26}OrthogonalLine(I_{26}, j_{52}) → m_{26}OrthogonalLine(I_{26}, m_{26}) → q_{26}OrthogonalLine(H_{26}, j_{52}) → r_{26}Intersect(q_{26}, r_{26}) → J_{26}Segment(I_{26}, G_{26}) → s_{26}Segment(I_{26}, J_{26}) → t_{26}Segment(J_{26}, H_{26}) → a_{27}Polygon(I_{26}, G_{26}, H_{26}, J_{26}) → poly1_{26}, i_{27}, g_{27}, h_{27}, j_{53}Circle(G_{27}, n) → k_{27}Point(k_{27}) → H_{27}Segment(G_{27}, H_{27}) → j_{54}Circle(G_{27}, i) → p_{27}OrthogonalLine(G_{27}, j_{54}) → l_{27}Intersect(p_{27}, l_{27}, 2) → I_{27}OrthogonalLine(I_{27}, j_{54}) → m_{27}OrthogonalLine(I_{27}, m_{27}) → q_{27}OrthogonalLine(H_{27}, j_{54}) → r_{27}Intersect(q_{27}, r_{27}) → J_{27}Segment(I_{27}, G_{27}) → s_{27}Segment(I_{27}, J_{27}) → t_{27}Segment(J_{27}, H_{27}) → a_{28}Polygon(I_{27}, G_{27}, H_{27}, J_{27}) → poly1_{27}, i_{28}, g_{28}, h_{28}, j_{55}Circle(G_{28}, n) → k_{28}Point(k_{28}) → H_{28}Segment(G_{28}, H_{28}) → j_{56}Circle(G_{28}, i) → p_{28}OrthogonalLine(G_{28}, j_{56}) → l_{28}Intersect(p_{28}, l_{28}, 2) → I_{28}OrthogonalLine(I_{28}, j_{56}) → m_{28}OrthogonalLine(I_{28}, m_{28}) → q_{28}OrthogonalLine(H_{28}, j_{56}) → r_{28}Intersect(q_{28}, r_{28}) → J_{28}Segment(I_{28}, G_{28}) → s_{28}Segment(I_{28}, J_{28}) → t_{28}Segment(J_{28}, H_{28}) → a_{29}Polygon(I_{28}, G_{28}, H_{28}, J_{28}) → poly1_{28}, i_{29}, g_{29}, h_{29}, j_{57}Circle(G_{29}, n) → k_{29}Point(k_{29}) → H_{29}Segment(G_{29}, H_{29}) → j_{58}Circle(G_{29}, i) → p_{29}OrthogonalLine(G_{29}, j_{58}) → l_{29}Intersect(p_{29}, l_{29}, 2) → I_{29}OrthogonalLine(I_{29}, j_{58}) → m_{29}OrthogonalLine(I_{29}, m_{29}) → q_{29}OrthogonalLine(H_{29}, j_{58}) → r_{29}Intersect(q_{29}, r_{29}) → J_{29}Segment(I_{29}, G_{29}) → s_{29}Segment(I_{29}, J_{29}) → t_{29}Segment(J_{29}, H_{29}) → a_{30}Polygon(I_{29}, G_{29}, H_{29}, J_{29}) → poly1_{29}, i_{30}, g_{30}, h_{30}, j_{59}Circle(G_{30}, n) → k_{30}Point(k_{30}) → H_{30}Segment(G_{30}, H_{30}) → j_{60}Circle(G_{30}, i) → p_{30}OrthogonalLine(G_{30}, j_{60}) → l_{30}Intersect(p_{30}, l_{30}, 2) → I_{30}OrthogonalLine(I_{30}, j_{60}) → m_{30}OrthogonalLine(I_{30}, m_{30}) → q_{30}OrthogonalLine(H_{30}, j_{60}) → r_{30}Intersect(q_{30}, r_{30}) → J_{30}Segment(I_{30}, G_{30}) → s_{30}Segment(I_{30}, J_{30}) → t_{30}Segment(J_{30}, H_{30}) → a_{31}Polygon(I_{30}, G_{30}, H_{30}, J_{30}) → poly1_{30}, i_{31}, g_{31}, h_{31}, j_{61}Circle(G_{31}, n) → k_{31}Point(k_{31}) → H_{31}Segment(G_{31}, H_{31}) → j_{62}Circle(G_{31}, i) → p_{31}OrthogonalLine(G_{31}, j_{62}) → l_{31}Intersect(p_{31}, l_{31}, 2) → I_{31}OrthogonalLine(I_{31}, j_{62}) → m_{31}OrthogonalLine(I_{31}, m_{31}) → q_{31}OrthogonalLine(H_{31}, j_{62}) → r_{31}Intersect(q_{31}, r_{31}) → J_{31}Segment(I_{31}, G_{31}) → s_{31}Segment(I_{31}, J_{31}) → t_{31}Segment(J_{31}, H_{31}) → a_{32}Polygon(I_{31}, G_{31}, H_{31}, J_{31}) → poly1_{31}, i_{32}, g_{32}, h_{32}, j_{63}Circle(G_{32}, n) → k_{32}Point(k_{32}) → H_{32}Segment(G_{32}, H_{32}) → j_{64}Circle(G_{32}, i) → p_{32}OrthogonalLine(G_{32}, j_{64}) → l_{32}Intersect(p_{32}, l_{32}, 2) → I_{32}OrthogonalLine(I_{32}, j_{64}) → m_{32}OrthogonalLine(I_{32}, m_{32}) → q_{32}OrthogonalLine(H_{32}, j_{64}) → r_{32}Intersect(q_{32}, r_{32}) → J_{32}Segment(I_{32}, G_{32}) → s_{32}Segment(I_{32}, J_{32}) → t_{32}Segment(J_{32}, H_{32}) → a_{33}Polygon(I_{32}, G_{32}, H_{32}, J_{32}) → poly1_{32}, i_{33}, g_{33}, h_{33}, j_{65}Circle(G_{33}, n) → k_{33}Point(k_{33}) → H_{33}Segment(G_{33}, H_{33}) → j_{66}Circle(G_{33}, i) → p_{33}OrthogonalLine(G_{33}, j_{66}) → l_{33}Intersect(p_{33}, l_{33}, 2) → I_{33}OrthogonalLine(I_{33}, j_{66}) → m_{33}OrthogonalLine(I_{33}, m_{33}) → q_{33}OrthogonalLine(H_{33}, j_{66}) → r_{33}Intersect(q_{33}, r_{33}) → J_{33}Segment(I_{33}, G_{33}) → s_{33}Segment(I_{33}, J_{33}) → t_{33}Segment(J_{33}, H_{33}) → a_{34}Polygon(I_{33}, G_{33}, H_{33}, J_{33}) → poly1_{33}, i_{34}, g_{34}, h_{34}, j_{67}Circle(G_{34}, n) → k_{34}Point(k_{34}) → H_{34}Segment(G_{34}, H_{34}) → j_{68}Circle(G_{34}, i) → p_{34}OrthogonalLine(G_{34}, j_{68}) → l_{34}Intersect(p_{34}, l_{34}, 2) → I_{34}OrthogonalLine(I_{34}, j_{68}) → m_{34}OrthogonalLine(I_{34}, m_{34}) → q_{34}OrthogonalLine(H_{34}, j_{68}) → r_{34}Intersect(q_{34}, r_{34}) → J_{34}Segment(I_{34}, G_{34}) → s_{34}Segment(I_{34}, J_{34}) → t_{34}Segment(J_{34}, H_{34}) → a_{35}Polygon(I_{34}, G_{34}, H_{34}, J_{34}) → poly1_{34}, i_{35}, g_{35}, h_{35}, j_{69}Circle(G_{35}, n) → k_{35}Point(k_{35}) → H_{35}Segment(G_{35}, H_{35}) → j_{70}Circle(G_{35}, i) → p_{35}OrthogonalLine(G_{35}, j_{70}) → l_{35}Intersect(p_{35}, l_{35}, 2) → I_{35}OrthogonalLine(I_{35}, j_{70}) → m_{35}OrthogonalLine(I_{35}, m_{35}) → q_{35}OrthogonalLine(H_{35}, j_{70}) → r_{35}Intersect(q_{35}, r_{35}) → J_{35}Segment(I_{35}, G_{35}) → s_{35}Segment(I_{35}, J_{35}) → t_{35}Segment(J_{35}, H_{35}) → a_{36}Polygon(I_{35}, G_{35}, H_{35}, J_{35}) → poly1_{35}, i_{36}, g_{36}, h_{36}, j_{71}Circle(G_{36}, n) → k_{36}Point(k_{36}) → H_{36}Segment(G_{36}, H_{36}) → j_{72}Circle(G_{36}, i) → p_{36}OrthogonalLine(G_{36}, j_{72}) → l_{36}Intersect(p_{36}, l_{36}, 2) → I_{36}OrthogonalLine(I_{36}, j_{72}) → m_{36}OrthogonalLine(I_{36}, m_{36}) → q_{36}OrthogonalLine(H_{36}, j_{72}) → r_{36}Intersect(q_{36}, r_{36}) → J_{36}Segment(I_{36}, G_{36}) → s_{36}Segment(I_{36}, J_{36}) → t_{36}Segment(J_{36}, H_{36}) → a_{37}Polygon(I_{36}, G_{36}, H_{36}, J_{36}) → poly1_{36}, i_{37}, g_{37}, h_{37}, j_{73}Polygon(E, F, D, A) → poly2, e_1, f_1, d_1, a_{38}Sequence(If[IsInRegion[Element[list1, n], poly2] ∧ IsInRegion[Element[List2, n], poly2] ∧ IsInRegion[Element[List3, n], poly2] ∧ IsInRegion[Element[List4, n], poly2], 1, 0], n, 1, 36) → list5Sum(list5) → zMidpoint(A, D) → KMidpoint(F, D) → L
AI Drawing Prompt Reference
Draw a rectangle and show the relationship between it and sine and cosine functions. Start by plotting the coordinate axes and finding their intersection point. Construct the rectangle using this point as a vertex. Then, find the midpoint of one side of the rectangle, draw perpendicular lines from this point to the opposite side, and locate the intersection point. Draw a circle with this point as the center, intersecting the axes at two points. Connect these points to the center, forming two equal right-angled triangles. Finally, connect these points to form two equal quadrilaterals, demonstrating the connection between the rectangle and trigonometric functions.
The prompt above was compiled from the original drawing commands and is for reference only.