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Diketahui tan β=2021​, tentukan besar sin β×csc β×cos β×sec β×cot β !

Pertanyaan

Diketahui tan space straight beta equals 21 over 20, tentukan besar sin space straight beta cross times csc space straight beta cross times cos space straight beta cross times sec space straight beta cross times cot space straight beta !

S. Difhayanti

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Prof. Dr. Hamka

Jawaban terverifikasi

Jawaban

besar sin space straight beta cross times csc space straight beta cross times cos space straight beta cross times sec space straight beta cross times cot space straight beta adalah 20 over 21.

Pembahasan

Diketahui : tan space straight beta equals 21 over 20.

Ditanya : besar sin space straight beta cross times csc space straight beta cross times cos space straight beta cross times sec space straight beta cross times cot space straight beta !

Jawab :
Dengan menggunakan teorema pythagoras untuk menentukan sisi miringnya.

table attributes columnalign right center left columnspacing 0px end attributes row cell mi squared end cell equals cell de squared plus sa squared end cell row mi equals cell square root of 21 squared plus 20 squared end root end cell row blank equals cell square root of 441 plus 400 end root end cell row blank equals cell square root of 841 end cell row blank equals 29 end table

Menghitung trigonometri setiap kuadran (sin space straight beta,space csc space straight beta, cos space straight beta, sec space straight beta,cot space straight beta).

tan space straight beta equals de over sa equals 21 over 20

sin space straight beta equals de over mi equals 21 over 29

space csc space straight beta equals 1 over sin equals mi over de equals 29 over 21

cos space straight beta equals sa over mi equals 20 over 29

sec space straight beta equals 1 over cos equals mi over sa equals 29 over 20

cot space straight beta equals 1 over tan equals sa over de equals 20 over 21

Maka besar dari fungsi trigonometri,

table attributes columnalign right center left columnspacing 0px end attributes row cell sin space straight beta cross times csc space straight beta cross times cos space straight beta cross times sec space straight beta cross times cot space straight beta end cell equals cell fraction numerator up diagonal strike 21 over denominator up diagonal strike 29 end fraction cross times fraction numerator up diagonal strike 29 over denominator up diagonal strike 21 end fraction cross times fraction numerator up diagonal strike 20 over denominator up diagonal strike 29 end fraction cross times fraction numerator up diagonal strike 29 over denominator up diagonal strike 20 end fraction cross times 20 over 21 end cell row blank equals cell 20 over 21 end cell end table

Jadi, besar sin space straight beta cross times csc space straight beta cross times cos space straight beta cross times sec space straight beta cross times cot space straight beta adalah 20 over 21.

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