Pertanyaan

Hitunglah masing-masing ekspresi berikut tanpa menggunakan kalkulator maupun tabel matematika. c. tan − 1 ( 3 3 )

Hitunglah masing-masing ekspresi berikut tanpa menggunakan kalkulator maupun tabel matematika.

c. $tan^{- 1} (\frac{3}{3})$

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Habis dalam

Klaim

D. Rajib

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Malang

Jawaban terverifikasi

Jawaban

.

$tan to the power of negative 1 end exponent space open parentheses fraction numerator square root of 3 over denominator 3 end fraction close parentheses equals straight pi over 6$ .

Pembahasan

Ingat kembali nilai-nilai trigonometri pada sudut istimewa berikut: Ditanyakan ekspresi . Misalkan: Ingat bahwa Maka Sehingga: Jadi, .

Ingat kembali nilai-nilai trigonometri pada sudut istimewa berikut:

Ditanyakan ekspresi $tan to the power of negative 1 end exponent space open parentheses fraction numerator square root of 3 over denominator 3 end fraction close parentheses$ .

Misalkan: $tan to the power of negative 1 end exponent space open parentheses fraction numerator square root of 3 over denominator 3 end fraction close parentheses equals theta$

Ingat bahwa y equals tan to the power of negative 1 end exponent space x left right double arrow tan space y equals x

Maka

$table attributes columnalign right center left columnspacing 0px end attributes row theta equals cell tan to the power of negative 1 end exponent space open parentheses fraction numerator square root of 3 over denominator 3 end fraction close parentheses end cell row cell tan space theta end cell equals cell fraction numerator square root of 3 over denominator 3 end fraction end cell row cell tan space theta end cell equals cell fraction numerator square root of 3 over denominator 3 end fraction cross times fraction numerator square root of 3 over denominator square root of 3 end fraction end cell row cell tan space theta end cell equals cell fraction numerator up diagonal strike 3 over denominator up diagonal strike 3 square root of 3 end fraction end cell row cell tan space theta end cell equals cell fraction numerator 1 over denominator square root of 3 end fraction end cell row cell tan space theta end cell equals cell tan space 30 degree end cell row theta equals cell 30 degree end cell row theta equals cell 30 degree cross times fraction numerator straight pi over denominator 180 degree end fraction space left parenthesis diubah space ke space rad right parenthesis end cell row theta equals cell straight pi over 6 end cell end table$

Sehingga:

$table attributes columnalign right center left columnspacing 0px end attributes row cell tan to the power of negative 1 end exponent space open parentheses fraction numerator square root of 3 over denominator 3 end fraction close parentheses end cell equals theta row blank equals cell straight pi over 6 end cell end table$

Jadi, $tan to the power of negative 1 end exponent space open parentheses fraction numerator square root of 3 over denominator 3 end fraction close parentheses equals straight pi over 6$ .