Pertanyaan

(SBMPTN 2014) Bila tan x = − 4 3 , 2 3 π < x < 2 π , maka sin ( 3 π − x ) = ...

(SBMPTN 2014)

Bila $tan x = - \frac{3}{4}, \frac{3 π}{2} < x < 2 π$ , maka $sin (\frac{π}{3} - x) = ...$

$fraction numerator open parentheses 2 square root of 3 plus 3 close parentheses over denominator 10 end fraction$
$fraction numerator open parentheses 3 square root of 3 plus 3 close parentheses over denominator 10 end fraction$
$fraction numerator open parentheses 4 square root of 3 plus 3 close parentheses over denominator 10 end fraction$
$fraction numerator open parentheses 3 square root of 3 minus 3 close parentheses over denominator 10 end fraction$
$fraction numerator open parentheses 4 square root of 3 minus 3 close parentheses over denominator 10 end fraction$

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Klaim

I. Roy

Master Teacher

Mahasiswa/Alumni Universitas Negeri Surabaya

Jawaban terverifikasi

Pembahasan

Ingat! sin (A - B) = sin A . cos B - cos A . sin B maka: (berada di kuadran IV), sehingga: dan Jadi,

Ingat!

sin (A - B) = sin A.cos B - cos A.sin B

maka:

$tan space x equals negative 3 over 4 comma fraction numerator 3 pi over denominator 2 end fraction less than x less than 2 pi$ (berada di kuadran IV), sehingga:

dan

Jadi,

$sin space open parentheses pi over 3 minus x close parentheses equals sin pi over 3. cos x minus cos pi over 3. sin x sin space open parentheses pi over 3 minus x close parentheses equals 1 half square root of 3.4 over 5 minus 1 half. open parentheses negative 3 over 5 close parentheses sin space open parentheses pi over 3 minus x close parentheses equals 1 over 10 open parentheses 4 square root of 3 plus 3 close parentheses sin space open parentheses pi over 3 minus x close parentheses equals fraction numerator open parentheses 4 square root of 3 plus 3 close parentheses over denominator 10 end fraction$