As equações trigonométricas são expressões de igualdade que envolvem as funções seno, cosseno e tangente e reduzem-se basicamente a três casos, que...

As equações trigonométricas são expressões de igualdade que envolvem as funções seno, cosseno e tangente e reduzem-se basicamente a três casos, que são: s e n left parenthesis alpha right parenthesis equals s e n left parenthesis beta right parenthesis comma space cos left parenthesis alpha right parenthesis equals cos left parenthesis beta right parenthesis space e space t g left parenthesis alpha right parenthesis equals t g left parenthesis beta right parenthesis . As equações baseiam-se em encontrar os valores dos arcos para os quais a igualdade é verificada. O conjunto solução da equação s e n left parenthesis x right parenthesis equals s e n space left parenthesis pi divided by 5 space right parenthesis é: a. S equals left curly bracket x element of R semicolon x equals begin inline style straight pi over 5 end style plus 2 k pi space o u space x equals begin inline style fraction numerator 4 straight pi over denominator 5 end fraction end style plus 2 k pi comma k element of straight integer numbers right curly bracket. b. S equals left curly bracket x element of R semicolon x equals begin inline style fraction numerator 11 pi over denominator 5 end fraction end style plus 2 k pi comma k element of R right curly bracket c. S equals left curly bracket x element of R semicolon x equals begin inline style fraction numerator 14 straight pi over denominator 5 end fraction end style plus 2 k pi comma k element of R right curly bracket. d. S equals left curly bracket x element of R semicolon x equals begin inline style fraction numerator 11 straight pi over denominator 5 end fraction end style plus k pi space o u space x equals begin inline style fraction numerator 14 straight pi over denominator 5 end fraction end style plus k pi comma k element of R right curly bracket. e. S equals left curly bracket x element of R semicolon x equals begin inline style straight pi over 5 end style plus 2 pi space o u space x equals begin inline style fraction numerator 4 straight pi over denominator 5 end fraction end style plus 2 pi right curly bracket.