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Jika cos x = 2 sin x, maka nilai sin x cos x adala...

Jika cos x = 2 sin x, maka nilai sin x cos x adalah...

  1. begin mathsize 12px style 1 fifth end style

  2. begin mathsize 12px style 1 fourth end style

  3. begin mathsize 12px style 1 third end style

  4. begin mathsize 12px style 2 over 5 end style

  5. begin mathsize 12px style 2 over 3 end style

Jawaban:

Perhatikan identitas trigonometri

begin mathsize 12px style tan space x equals fraction numerator sin space x over denominator cos space x end fraction equals fraction numerator d e p a n over denominator s a m p i n g end fraction space midline horizontal ellipsis space open parentheses 1 close parentheses  D a r i space s o a l comma space 2 space sin space x equals space cos space x space open parentheses k e d u a space r u a s space d i b a g i space cos space x close parentheses  fraction numerator 2 space sin space x over denominator cos space x end fraction equals fraction numerator cos space x over denominator cos space x end fraction  fraction numerator 2 space sin space x over denominator cos space x end fraction equals 1 end style

 

tan x = 1

begin mathsize 12px style tan space x equals 1 half equals fraction numerator s i s i space d e p a n over denominator s i s i space s a m p i n g end fraction end style

Dapat diperoleh sisi depan = 1, sisi samping = 2

Sisi miring = Error converting from MathML to accessible text.

sin x . cos x = begin mathsize 12px style fraction numerator 1 over denominator square root of 5 end fraction times fraction numerator begin display style 2 end style over denominator begin display style square root of 5 end style end fraction equals 2 over 5 end style

 

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