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الحل العام للمعادلة المثلثية اهداء الاستاذ ابراهيم الاحمدى ابراهيم
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الحل العام للمعادلة المثلثية اهداء الاستاذ ابراهيم الاحمدى ابراهيم
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الحل العام للمعادلة المثلثية اهداء الاستاذ ابراهيم الاحمدى ابراهيم
1.
اﻟﺤﻞاﻟﻌﺎم ﻟﻠﻤﻌﺎدﻟﺔاﻟﻤﺜﻠﺜﻴﺔ ﺗــﺄﻟﻴـﻒ 01120930112
2.
etn.alafdal.4mathtop.www1اﻟﻤﺘﻘﺪﻣﺔ اﻟﺮﯾﺎﺿﯿﺎت ﻣﻨﺘﺪى 0112
093 0112 اﻟﺮﯾﺎﺿﯿﺎت ﺧﺒﯿﺮ ﻣﻌﻠﻢ اﺑﺮاھﯿﻢ اﻷﺣﻤﺪى اﺑﺮاھﯿﻢ / اﻷﺳﺘﺎذ اﻋﺪاد اﻟﻤﺜﻠﺜﯿﺔ ﻟﻠﻤﻌﺎدﻟﺔ اﻟﻌﺎم اﻟﺤﻞ βﺟﺎ = α ﺟﺎ اﻟﺼﻮرة ﻋﻠﻰ اﻟﺘﻰ اوﻻ:اﻟﻤﻌﺎدﻟﺔ ﯾﻜﻮن اﻟﻌﺎم اﻟﺤﻞα=ﻥﺐ+)-1(ﻥβ اﻟﺒﺮھﺎن اﻣﺎﺟﺎα=ﺟﺎβﺉα=٢ﻥﺐ+β ﺉα=زوﺟﻰ ﻋﺪد×ﺐ+β اوﺟﺎα=ﺟﺎ)ﺐ-β(ﺉα=٢ﻥﺐ+ﺐ-β ﺉα) =٢ﻥ+1(ﺐ-β ﺉα=ﻓﺮدى ﻋﺪد×ﺐ-β ﺇاﻟﺤﻞﯾﻜﻮن اﻟﻌﺎمα=ﻥﺐ+)-1(ﻥβ ﺗﻄﺒﯿﻘﻰ ﻣﺜﺎل ﻟﻠﻤﻌﺎدﻟﺔ اﻟﻌﺎم اﻟﺤﻞ أوﺟﺪ:ﺟﺎ٢θ=ﺟﺘﺎθ اﻟﺤﻞ ﺟﺎ٢θ=ﺟﺎ)-θ( ٢θ=ﻥﺐ+)-1(ﻥ)-θ( ﻛﺎﻧﺖ اذانﻓﺎن زوﺟﻰ٢θ=ﻥﺐ) +-θ( ٣θ=ﻥﺐ+ﺉθ+ = ﻛﺎﻧﺖ اذانﻓﺮدىﻓﺎن٢θ=ﻥﺐ-)-θ( ٢θ=ﻥﺐ-+θﺉθ=ﻥﺐ- ﺐ ٢ﺐ ٢ ﺐ ٢ ﺐ ٢ ﻥﺐ ٣ ﺐ ٦ ﺐ ٢ ﺐ ٢ ﺐ ٢
3.
etn.alafdal.4mathtop.www2اﻟﻤﺘﻘﺪﻣﺔ اﻟﺮﯾﺎﺿﯿﺎت ﻣﻨﺘﺪى 0112
093 0112 اﻟﺮﯾﺎﺿﯿﺎت ﺧﺒﯿﺮ ﻣﻌﻠﻢ اﺑﺮاھﯿﻢ اﻷﺣﻤﺪى اﺑﺮاھﯿﻢ / اﻷﺳﺘﺎذ اﻋﺪاد βﺟﺘﺎ = α ﺟﺘﺎ اﻟﺼﻮرة ﻋﻠﻰ اﻟﺘﻰ ﺛﺎﻧﯿﺎ:اﻟﻤﻌﺎدﻟﺔ ﯾﻜﻮن اﻟﻌﺎم اﻟﺤﻞα=٢ﻥﺐ±β اﻟﺒﺮھﺎن اﻣﺎﺟﺘﺎα=ﺟﺘﺎβﺉα=٢ﻥﺐ+β ﺉα=ﻋﺪدزوﺟﻰ×ﺐ+β اوﺟﺘﺎα=ﺟﺘﺎ)٢ﺐ-β(ﺉα=٢ﻥﺐ+٢ﺐ-β ﺉα) =٢ﻥ+٢(ﺐ-β ﺉα=ﻋﺪدزوﺟﻰ×ﺐ-β ﺇاﻟﺤﻞﯾﻜﻮن اﻟﻌﺎمα=٢ﻥﺐ±β ﺗﻄﺒﯿﻘﻰ ﻣﺜﺎل ﻟﻠﻤﻌﺎدﻟﺔ اﻟﻌﺎم اﻟﺤﻞ أوﺟﺪ:ﺟﺎ٢θ=ﺟﺘﺎθ اﻟﺤﻞ ﺟﺘﺎ)-٢θ(=ﺟﺘﺎθ θ=٢ﻥﺐ±)-٢θ( اﻣﺎθ=٢ﻥﺐ) +-٢θ( ٣θ=٢ﻥﺐ+ﺉθ=+ اوθ=٢ﻥﺐ-)-٢θ( θ=٢ﻥﺐ-+٢θ -θ=٢ﻥﺐ-ﺉθ=-٢ﻥﺐ+ ﺐ ٢ﺐ ٢ ﺐ ٢ ﺐ ٢ ٢ﻥﺐ ٣ ﺐ ٦ ﺐ ٢ ﺐ ٢ ﺐ ٢ ﺐ ٢
4.
etn.alafdal.4mathtop.www3اﻟﻤﺘﻘﺪﻣﺔ اﻟﺮﯾﺎﺿﯿﺎت ﻣﻨﺘﺪى 0112
093 0112 اﻟﺮﯾﺎﺿﯿﺎت ﺧﺒﯿﺮ ﻣﻌﻠﻢ اﺑﺮاھﯿﻢ اﻷﺣﻤﺪى اﺑﺮاھﯿﻢ / اﻷﺳﺘﺎذ اﻋﺪاد βظﺎ = α ظﺎ اﻟﺼﻮرة ﻋﻠﻰ اﻟﺘﻰ ﺛﺎﻟﺜﺎ:اﻟﻤﻌﺎدﻟﺔ ﯾﻜﻮن اﻟﻌﺎم اﻟﺤﻞα=ﻥﺐ+β اﻟﺒﺮھﺎن اﻣﺎظﺎα=ظﺎβﺉα=٢ﻥﺐ+β ﺉα=ﻋﺪدزوﺟﻰ×ﺐ+β اوظﺎα=ظﺎ)ﺐ+β(ﺉα=٢ﻥﺐ+ﺐ+β ﺉα) =٢ﻥ+1(ﺐ+β ﺉα=ﻋﺪدﻓﺮدى+β ﺇاﻟﺤﻞﯾﻜﻮن اﻟﻌﺎمα=ﻥﺐ+β ﺗﻄﺒﯿﻘﻰ ﻣﺜﺎل ﻟﻠﻤﻌﺎدﻟﺔ اﻟﻌﺎم اﻟﺤﻞ أوﺟﺪ:ظﺎ٢θ=ظﺘﺎθ اﻟﺤﻞ ظﺎ٢θ=ظﺎ)-θ( ٢θ=ﻥﺐ) +-θ( ٣θ=ﻥﺐ+ θ+ = ﺐ ٢ﺐ ٢ﺐ ٢ ﺐ ٦ ﻥﺐ ٣
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