Pertanyaan

Tanpa alat bantu, tentukan nilai dari: tan 4 3 π − cot 6 5 π + sin 6 11 π + cos 3 5 π

Tanpa alat bantu, tentukan nilai dari:

$tan \frac{3 π}{4} - cot \frac{5 π}{6} + sin \frac{11 π}{6} + cos \frac{5 π}{3}$

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Jawaban terverifikasi

Jawaban

nilai dari adalah .

nilai dari $tan space fraction numerator 3 straight pi over denominator 4 end fraction minus cot fraction numerator 5 straight pi over denominator 6 end fraction plus sin space fraction numerator 11 straight pi over denominator 6 end fraction plus cos space fraction numerator 5 straight pi over denominator 3 end fraction$ adalah negative 1 plus square root of 3

Pembahasan

Ingat kembali: Sudut berelasi dikuadran I. Sudut berelasi dikuadran IV. Sehingga, diperoleh perhitungan berikut. Maka, Jadi,nilai dari adalah .

Ingat kembali:

Sudut berelasi dikuadran I.

table attributes columnalign right center left columnspacing 0px end attributes row cell tan space alpha end cell equals cell negative tan space open parentheses 180 degree minus alpha close parentheses end cell row cell cot space alpha end cell equals cell negative cot space open parentheses 180 degree minus alpha close parentheses end cell end table

Sudut berelasi dikuadran IV.

table attributes columnalign right center left columnspacing 0px end attributes row cell sin space alpha end cell equals cell negative sin space open parentheses 360 degree minus alpha close parentheses end cell row cell cos space alpha end cell equals cell cos space open parentheses 360 degree minus alpha close parentheses end cell end table

Sehingga, diperoleh perhitungan berikut.

$table attributes columnalign right center left columnspacing 0px end attributes row cell tan space fraction numerator 3 straight pi over denominator 4 end fraction end cell equals cell tan space 135 degree end cell row blank equals cell negative tan space 45 degree end cell row blank equals cell negative 1 end cell row cell cot fraction numerator 5 straight pi over denominator 6 end fraction end cell equals cell cot space 150 degree end cell row blank equals cell negative cot space 30 degree end cell row blank equals cell negative square root of 3 end cell row cell sin space fraction numerator 11 straight pi over denominator 6 end fraction end cell equals cell sin space 330 degree end cell row blank equals cell negative sin space 30 degree end cell row blank equals cell negative 1 half end cell row cell cos space fraction numerator 5 straight pi over denominator 3 end fraction end cell equals cell cos space 300 degree end cell row blank equals cell cos space 60 degree end cell row blank equals cell 1 half end cell end table$

Maka,

$table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell tan space fraction numerator 3 straight pi over denominator 4 end fraction minus cot fraction numerator 5 straight pi over denominator 6 end fraction plus sin space fraction numerator 11 straight pi over denominator 6 end fraction plus cos space fraction numerator 5 straight pi over denominator 3 end fraction end cell row blank equals cell negative 1 minus open parentheses negative square root of 3 close parentheses plus open parentheses negative 1 half close parentheses plus 1 half end cell row blank equals cell negative 1 plus square root of 3 end cell end table$

Jadi, nilai dari $tan space fraction numerator 3 straight pi over denominator 4 end fraction minus cot fraction numerator 5 straight pi over denominator 6 end fraction plus sin space fraction numerator 11 straight pi over denominator 6 end fraction plus cos space fraction numerator 5 straight pi over denominator 3 end fraction$ adalah negative 1 plus square root of 3 .