Tanpa menggunakan tabel matematika dan kalkulator, hitunglah setiap bentuk berikut. g. tan 105∘

Pertanyaan

Tanpa menggunakan tabel matematika dan kalkulator, hitunglah setiap bentuk berikut.

g. $\tan\;105^\circ$

H. Janatu

Master Teacher

Mahasiswa/Alumni Universitas Riau

Jawaban terverifikasi

Jawaban

diperoleh $\begin{array}{rcl}\tan\;105^\circ&=&-2-\sqrt3\end{array}$ .

Pembahasan

Ingat rumus jumlah dua sudut pada tangen :

$table attributes columnalign right center left columnspacing 0px end attributes row cell tan space left parenthesis A plus B right parenthesis end cell equals cell fraction numerator tan space A plus tan space B over denominator 1 minus tan space A space tan space B end fraction end cell end table$

Maka,

$table attributes columnalign right center left columnspacing 0px end attributes row cell tan space 105 degree end cell equals cell tan space left parenthesis 45 degree plus 60 degree right parenthesis end cell row blank equals cell fraction numerator tan space 45 degree plus tan space 60 degree over denominator 1 minus tan space 45 degree space tan space 60 degree end fraction end cell row blank equals cell fraction numerator 1 plus square root of 3 over denominator 1 minus 1 times square root of 3 end fraction end cell row blank equals cell fraction numerator 1 plus square root of 3 over denominator 1 minus square root of 3 end fraction cross times fraction numerator 1 plus square root of 3 over denominator 1 plus square root of 3 end fraction end cell row blank equals cell fraction numerator 1 plus 2 square root of 3 plus 3 over denominator 1 minus 3 end fraction end cell row blank equals cell fraction numerator 4 plus 2 square root of 3 over denominator negative 2 end fraction end cell row blank equals cell negative 2 minus square root of 3 end cell end table$

Jadi, diperoleh $\begin{array}{rcl}\tan\;105^\circ&=&-2-\sqrt3\end{array}$ .