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Hitung ekspresi berikut tanpa menggunakan kalkulator maupun tabel trigonometri. b. secan [ sin − 1 ( − 2 1 ​ ) + cos − 1 ( 0 ) + tan − 1 ( 3 ​ ) ]

Hitung ekspresi berikut tanpa menggunakan kalkulator maupun tabel trigonometri.

b.   

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S. Nur

Master Teacher

Jawaban terverifikasi

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 secan space open square brackets sin to the power of negative 1 end exponent space open parentheses negative 1 half close parentheses plus cos to the power of negative 1 end exponent space open parentheses 0 close parentheses plus tan to the power of negative 1 end exponent space open parentheses square root of 3 close parentheses close square brackets equals negative 2.

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Pembahasan

Ingat kembali nilai-nilai trigonometri pada sudut istimewa berikut: Diketahui ekspresi . Misalkan: - Untuk - Untuk - Untuk Maka: Jadi, .

Ingat kembali nilai-nilai trigonometri pada sudut istimewa berikut:

Diketahui ekspresi s e c a n space open square brackets sin to the power of negative 1 end exponent space open parentheses negative 1 half close parentheses plus cos to the power of negative 1 end exponent space open parentheses 0 close parentheses plus tan to the power of negative 1 end exponent space open parentheses square root of 3 close parentheses close square brackets. Misalkan:

- Untuk sin to the power of negative 1 end exponent space open parentheses negative 1 half close parentheses 

table attributes columnalign right center left columnspacing 0px end attributes row alpha equals cell sin to the power of negative 1 end exponent space open parentheses negative 1 half close parentheses end cell row cell sin space alpha end cell equals cell negative 1 half end cell row cell sin space alpha end cell equals cell sin space open parentheses negative 30 degree close parentheses end cell row alpha equals cell negative 30 degree end cell end table 

- Untuk cos to the power of negative 1 end exponent space open parentheses 0 close parentheses 

table attributes columnalign right center left columnspacing 0px end attributes row beta equals cell cos to the power of negative 1 end exponent space open parentheses 0 close parentheses end cell row cell cos space beta end cell equals 0 row cell cos space beta end cell equals cell 90 degree end cell row beta equals cell 90 degree end cell end table 

- Untuk tan to the power of negative 1 end exponent space open parentheses square root of 3 close parentheses 

table attributes columnalign right center left columnspacing 0px end attributes row gamma equals cell tan to the power of negative 1 end exponent space open parentheses square root of 3 close parentheses end cell row cell tan space gamma end cell equals cell square root of 3 end cell row cell tan space gamma end cell equals cell tan space 60 degree end cell row gamma equals cell 60 degree end cell end table 

Maka:

begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell secan space open square brackets sin to the power of negative 1 end exponent space open parentheses negative 1 half close parentheses plus cos to the power of negative 1 end exponent space open parentheses 0 close parentheses plus tan to the power of negative 1 end exponent space open parentheses square root of 3 close parentheses close square brackets end cell equals cell secan space open parentheses alpha plus beta plus gamma close parentheses end cell row blank equals cell secan space open parentheses negative 30 degree plus 90 degree plus 60 degree close parentheses end cell row blank equals cell secan space 120 degree end cell row blank equals cell fraction numerator 1 over denominator cos space 120 degree end fraction end cell row blank equals cell fraction numerator 1 over denominator cos space open parentheses 90 degree plus 30 degree close parentheses end fraction end cell row blank equals cell fraction numerator 1 over denominator negative sin space 30 degree end fraction end cell row blank equals cell fraction numerator 1 over denominator negative begin display style 1 half end style end fraction end cell row blank equals cell negative 2 end cell end table end style 

Jadi, secan space open square brackets sin to the power of negative 1 end exponent space open parentheses negative 1 half close parentheses plus cos to the power of negative 1 end exponent space open parentheses 0 close parentheses plus tan to the power of negative 1 end exponent space open parentheses square root of 3 close parentheses close square brackets equals negative 2.

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