حمّل تطبيق منهاجي الجديد

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  إجابات أتحقق من فهمي

إجابات أتحقق من فهمي

المتطابقات المثلثية – 1

المتطابقات المثلثية الأساسية

أتحقق من فهمي صفحة (56):

أجد قيمة tan Ɵ إذا كان begin mathsize 20px style pi less than theta less than fraction numerator 3 pi over denominator 2 end fraction comma space sec invisible function application space theta equals negative 3 over 2 end style

begin mathsize 20px style tan invisible function application space theta equals fraction numerator 2 over denominator square root of 5 end fraction end style

أتحقق من فهمي صفحة (57):

أبسط كلاً من المقادير المثلثية الآتية:

a) sin x (csc x – sin x)

begin mathsize 20px style table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell sin invisible function application space x left parenthesis csc invisible function application space x minus sin invisible function application space x right parenthesis end cell cell equals sin invisible function application space x italic space csc invisible function application space x minus sin squared invisible function application space x end cell row blank cell equals sin invisible function application space x left parenthesis fraction numerator 1 over denominator sin invisible function application space x end fraction right parenthesis minus sin squared invisible function application space x end cell row blank cell equals 1 minus sin squared invisible function application space x end cell row blank cell equals cos squared invisible function application space x end cell end table end style

b) begin mathsize 20px style 1 plus fraction numerator sin invisible function application space x over denominator cos invisible function application space x end fraction plus fraction numerator cos invisible function application space x over denominator 1 plus sin invisible function application space x end fraction end style

begin mathsize 20px style table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell 1 plus fraction numerator sin invisible function application x over denominator cos invisible function application x end fraction plus fraction numerator cos invisible function application x over denominator 1 plus sin invisible function application x end fraction end cell cell equals fraction numerator cos invisible function application x left parenthesis 1 plus sin invisible function application x right parenthesis plus sin invisible function application x left parenthesis 1 plus sin invisible function application x right parenthesis plus cos squared invisible function application x over denominator cos invisible function application x left parenthesis 1 plus sin invisible function application x right parenthesis end fraction end cell row blank cell equals fraction numerator cos invisible function application x left parenthesis 1 plus sin invisible function application x right parenthesis plus sin invisible function application x plus sin squared invisible function application x plus cos squared invisible function application x over denominator cos invisible function application x left parenthesis 1 plus sin invisible function application x right parenthesis end fraction end cell row blank cell equals fraction numerator cos invisible function application x left parenthesis 1 plus sin invisible function application x right parenthesis plus sin invisible function application x plus 1 over denominator cos invisible function application x left parenthesis 1 plus sin invisible function application x right parenthesis end fraction end cell row blank cell equals fraction numerator left parenthesis cos invisible function application x plus 1 right parenthesis left parenthesis 1 plus sin invisible function application x right parenthesis over denominator cos invisible function application x left parenthesis 1 plus sin invisible function application x right parenthesis end fraction end cell row blank cell equals 1 plus sec invisible function application x end cell end table end style

c) begin mathsize 20px style sin invisible function application space left parenthesis pi over 2 minus x right parenthesis space sec invisible function application space x end style

begin mathsize 20px style sin invisible function application left parenthesis pi over 2 minus x right parenthesis sec invisible function application space x equals cos invisible function application space x left parenthesis fraction numerator 1 over denominator cos invisible function application space x end fraction right parenthesis equals 1 end style

 

أتحقق من فهمي صفحة (57):

أعيد كتابة begin mathsize 20px style fraction numerator 1 over denominator 1 plus cos invisible function application space x end fraction end style بحيث لا يحوي كسراً.

begin mathsize 20px style table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell fraction numerator 1 over denominator 1 plus cos invisible function application space x end fraction end cell cell equals fraction numerator 1 minus cos invisible function application space x over denominator 1 minus cos squared invisible function application space x end fraction end cell row blank cell equals fraction numerator 1 minus cos invisible function application space x over denominator sin squared invisible function application space x end fraction end cell row blank cell equals fraction numerator 1 over denominator sin squared invisible function application space x end fraction minus fraction numerator cos invisible function application space x over denominator sin invisible function application space x end fraction cross times fraction numerator 1 over denominator sin invisible function application space x end fraction end cell row blank cell equals csc squared invisible function application space x minus cot invisible function application space x italic space csc invisible function application space x end cell end table end style

 

أتحقق من فهمي صفحة (60):

أثبت صحة كل من المتطابقات الآتية:

a) cot x cos x = csc x – sin x

begin mathsize 20px style table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell fraction numerator 1 over denominator 1 plus cos invisible function application space x end fraction end cell cell equals fraction numerator 1 minus cos invisible function application space x over denominator 1 minus cos squared invisible function application space x end fraction end cell row blank cell equals fraction numerator 1 minus cos invisible function application space x over denominator sin squared invisible function application space x end fraction end cell row blank cell equals fraction numerator 1 over denominator sin squared invisible function application space x end fraction minus fraction numerator cos invisible function application space x over denominator sin invisible function application space x end fraction cross times fraction numerator 1 over denominator sin invisible function application space x end fraction end cell row blank cell equals csc squared invisible function application space x minus cot invisible function application space x italic space csc invisible function application space x end cell end table end style

 

 

إعداد : شبكة منهاجي التعليمية

03 / 03 / 2024

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