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Diketahui tan 17∘=247​ (nilai pembulatan). Tentukan nilai bentuk trigonometri berikut. a. cos 17∘ sin 73∘−sin 17∘ tan 73∘  b. sec 287∘cosec 163∘+tan 343∘​

Pertanyaan

Diketahui tan space 17 degree equals 7 over 24 (nilai pembulatan). Tentukan nilai bentuk trigonometri berikut.

a. cos space 17 degree space sin space 73 degree minus sin space 17 degree space tan space 73 degree 

b. fraction numerator cosec space 163 degree plus tan space 343 degree over denominator sec space 287 degree end fraction 

S. Amamah

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

Jawaban terverifikasi

Jawaban

nilai dari fraction numerator cosec space 163 degree plus tan space 343 degree over denominator sec space 287 degree end fraction  adalah 551 over 600.

Pembahasan

Ingat kembali definisi sincostan, dan : 

table attributes columnalign right center left columnspacing 0px end attributes row cell sin space straight theta end cell equals cell fraction numerator sisi space depan over denominator sisi space miring end fraction end cell row cell cos space straight theta end cell equals cell fraction numerator sisi space samping over denominator sisi space miring end fraction end cell row cell tan space straight theta end cell equals cell fraction numerator sisi space depan over denominator sisi space samping end fraction end cell row cell cotan space straight theta end cell equals cell fraction numerator sisi space samping over denominator sisi space depan end fraction end cell row cell cosec space straight theta end cell equals cell fraction numerator sisi space miring over denominator sisi space depan end fraction end cell end table   

Ingat kembali 

table attributes columnalign right center left columnspacing 0px end attributes row cell sin space open parentheses 90 degree minus straight alpha close parentheses end cell equals cell cos space straight alpha end cell row cell tan space open parentheses 90 degree minus straight alpha close parentheses end cell equals cell cotan space straight alpha end cell row cell tan space open parentheses 360 degree minus straight alpha close parentheses end cell equals cell negative tan space straight alpha end cell row cell cosec space open parentheses 180 degree minus straight alpha close parentheses end cell equals cell cosec space straight alpha end cell row cell sec space open parentheses 270 degree plus straight alpha close parentheses end cell equals cell cosec space straight alpha end cell end table  

Diketahui tan space 17 degree equals 7 over 24 dengan menggunakan teorema Pythagoras maka diperoleh sisi miring:

table attributes columnalign right center left columnspacing 0px end attributes row cell sisi space miring end cell equals cell square root of 24 squared plus 7 squared end root end cell row blank equals cell square root of 576 plus 49 end root end cell row blank equals cell square root of 625 end cell row blank equals 25 end table 

a. sehingga diperoleh 

cos space 17 degree space sin space 73 degree minus sin space 17 degree space tan space 73 degree equals cos space 17 degree space sin space open parentheses 90 degree minus space 17 degree close parentheses minus sin space 17 degree space tan space open parentheses 90 degree minus space 17 degree close parentheses equals cos space 17 degree space cos space 17 degree minus sin space 17 degree space cotan space 17 degree equals 24 over 25 times 24 over 25 minus 7 over 25 times 24 over 7 equals space 576 over 625 minus 24 over 25 equals fraction numerator 576 minus 600 over denominator 625 end fraction equals negative 24 over 625 

Dengan demikian nilai cos space 17 degree space sin space 73 degree minus sin space 17 degree space tan space 73 degree adalah negative 24 over 625.

b. sehingga diperoleh

begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator cosec space 163 degree plus tan space 343 degree over denominator sec space 287 degree end fraction end cell equals cell fraction numerator cosec space open parentheses 180 degree minus 17 degree close parentheses plus tan space open parentheses 360 degree minus 17 degree close parentheses over denominator sec space open parentheses 270 degree plus 17 degree close parentheses end fraction end cell row blank equals cell fraction numerator cos e c space 17 degree plus open parentheses negative tan space 17 degree close parentheses over denominator cos e c space 17 degree end fraction end cell row blank equals cell fraction numerator begin display style 25 over 7 end style minus begin display style 7 over 24 end style over denominator begin display style 25 over 7 end style end fraction end cell row blank equals cell fraction numerator begin display style fraction numerator 600 minus 49 over denominator 168 end fraction end style over denominator begin display style 25 over 7 end style end fraction end cell row blank equals cell fraction numerator begin display style 551 over 168 end style over denominator begin display style 25 over 7 end style end fraction end cell row blank equals cell fraction numerator 551 over denominator up diagonal strike 168 end fraction cross times fraction numerator up diagonal strike 7 over denominator 25 end fraction end cell row blank equals cell 551 over 600 end cell end table end style 

Dengan demikian nilai dari fraction numerator cosec space 163 degree plus tan space 343 degree over denominator sec space 287 degree end fraction  adalah 551 over 600.

430

4.3 (6 rating)

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