Roboguru

Bila tanx=−43​,23x​<x<2π, maka sin(3π​−x) = ....

Pertanyaan

Bila begin mathsize 14px style tan space straight x equals negative 3 over 4 comma space space space fraction numerator 3 straight x over denominator 2 end fraction less than straight x less than 2 straight pi end style, maka begin mathsize 14px style sin space open parentheses begin inline style straight pi over 3 end style minus x close parentheses end style = ....

  1. begin mathsize 14px style fraction numerator open parentheses 2 square root of 3 plus 3 close parentheses over denominator 10 end fraction end style

  2. begin mathsize 14px style fraction numerator open parentheses 3 square root of 3 plus 3 close parentheses over denominator 10 end fraction end style

  3. begin mathsize 14px style fraction numerator open parentheses 4 square root of 3 plus 3 close parentheses over denominator 10 end fraction end style

  4. begin mathsize 14px style fraction numerator open parentheses 3 square root of 3 minus 3 close parentheses over denominator 10 end fraction end style

  5. begin mathsize 14px style fraction numerator open parentheses 4 square root of 3 minus 3 close parentheses over denominator 10 end fraction end style

Pembahasan:

begin mathsize 14px style tan space invisible function application straight x equals negative 3 over 4  Buat space segitiganya comma space dengan space konsep colon space tan invisible function application space straight x equals fraction numerator sisi straight space depan over denominator sisi straight space samping end fraction end style

begin mathsize 14px style Sisi straight space miring equals square root of 3 squared plus 4 squared end root equals 5  Karena space intervalnya space fraction numerator 3 straight pi over denominator 2 end fraction less than straight x less than 2 straight pi comma space maka space ada space di space kuadaran space  IV comma space di space mana space nilai space sinusnya space negatif space dan space cosinusnya space positif comma space  sehingga colon  sin invisible function application space straight x equals negative 3 over 5  cos invisible function application space straight x equals 4 over 5    sin invisible function application left parenthesis straight A minus straight B right parenthesis equals sin space invisible function application straight A space cos invisible function application space straight B minus cos space invisible function application straight A space sin space invisible function application straight B  sin invisible function application open parentheses straight pi over 3 minus straight x close parentheses equals sin invisible function application space straight pi over 3 space cos space invisible function application straight x minus cos invisible function application straight pi over 3 space sin space invisible function application straight x  space space space space space space space space space space space space space space space space space space space equals 1 half square root of 3 straight space.4 over 5 minus 1 half straight space. straight space open parentheses negative 3 over 5 close parentheses  space space space space space space space space space space space space space space space space space space space equals 4 over 10 square root of 3 plus 3 over 10  space space space space space space space space space space space space space space space space space space space equals fraction numerator open parentheses 4 square root of 3 plus 3 close parentheses over denominator 10 end fraction end style

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Terakhir diupdate 05 Oktober 2021

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Nilai cot105∘tan15∘ adalah....

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