Pertanyaan

Diketahui sin β = 9 4 , tentukan sin 2 β + cos 2 β + tan 2 β

Diketahui $sin β = \frac{4}{9}$ , tentukan

$sin^{2} β + cos^{2} β + tan^{2} β$

L. Rante

Master Teacher

Mahasiswa/Alumni Universitas Negeri Makassar

Jawaban terverifikasi

Jawaban

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sin squared beta plus cos squared beta plus tan squared beta equals 81 over 65

Pembahasan

Berdasarkan defenisi sinus . Karena , maka Dengan menggunakan teorema Pythagoras, diperoleh panjang sisi samping yaitu Jadi Jadi, .

Berdasarkan defenisi sinus $sin space beta equals fraction numerator panjang space sisi space depan space angle beta over denominator panjang space sisi space miring end fraction$ . Karena sin space beta equals 4 over 9 , maka

Panjang space sisi space depan space angle beta space equals 4 Panjang space sisi space miring space equals 9

Dengan menggunakan teorema Pythagoras, diperoleh panjang sisi samping angle beta yaitu

table attributes columnalign right center left columnspacing 0px end attributes row cell panjang space sisi space samping space angle beta end cell equals cell square root of 9 squared minus 4 squared end root end cell row blank equals cell square root of 81 minus 16 end root end cell row blank equals cell square root of 65 end cell end table

Jadi

$table attributes columnalign right center left columnspacing 0px end attributes row cell sin squared beta plus cos squared beta plus tan squared beta end cell equals cell open parentheses 4 over 9 close parentheses squared plus open parentheses fraction numerator square root of 65 over denominator 9 end fraction close parentheses squared plus open parentheses fraction numerator 4 over denominator square root of 65 end fraction close parentheses squared end cell row blank equals cell 16 over 81 plus 65 over 81 plus 16 over 65 end cell row blank equals cell fraction numerator 16 plus 65 over denominator 81 end fraction plus 16 over 65 end cell row blank equals cell 81 over 81 plus 16 over 65 end cell row blank equals cell 1 plus 16 over 65 end cell row blank equals cell fraction numerator 65 plus 16 over denominator 65 end fraction end cell row blank equals cell 81 over 65 end cell end table$

Jadi, sin squared beta plus cos squared beta plus tan squared beta equals 81 over 65 .