Abin da ke kusa da kusurwoyi: definition, theorem, Properties

A cikin wannan ɗaba'ar, za mu yi la'akari da menene kusurwoyin da ke kusa, mu ba da tsarin ka'idar game da su (gami da sakamakonsa), da kuma lissafa abubuwan trigonometric na kusa da kusurwoyi.

Ma'anar sasanninta kusa

Ana kiran kusurwoyi biyu maƙwabta waɗanda ke samar da madaidaiciyar layi tare da ɓangarorinsu na waje dab da. A cikin hoton da ke ƙasa, waɗannan su ne kusurwoyi α и β.

Idan kusurwoyi biyu suna raba juzu'i ɗaya da gefe, suna dab da. A wannan yanayin, yankuna na ciki na waɗannan sasanninta bai kamata su shiga tsakani ba.

Ka'idar gina kusurwar kusa

Muna shimfiɗa ɗaya daga cikin bangarorin kusurwa ta hanyar gabaɗaya, sakamakon haka an kafa sabon kusurwa, kusa da na asali.

Matsakaicin ka'idar kusurwa

Jimlar ma'aunin ma'aunin kusurwoyi na kusa shine 180°.

Kusurwar da ke kusa 1 + Madaidaicin kwana 2 = 180°

Misali 1

Ɗaya daga cikin kusurwoyi na kusa shine 92 °, menene ɗayan?

Maganin, bisa ga ka'idar da aka tattauna a sama, a bayyane yake:

Matsakaicin kusurwa 2 = 180° - Madaidaicin kwana 1 = 180° – 92° = 88°.

Sakamako daga theorem:

• Kusurwoyi madaidaici na kusurwoyi biyu daidai suna daidai da juna.
• Idan kwana yana kusa da kusurwar dama (90°), to shima 90° ne.
• Idan kwana yana kusa da wani m, to ya fi 90 °, watau bebe ne (kuma akasin haka).

Misali 2

Bari mu ce muna da kwana kusa da 75°. Dole ne ya zama fiye da 90 °. Mu duba.

Amfani da ka'idar, mun sami darajar kusurwa ta biyu:

180° – 75° = 105°.

105°> 90°, sabili da haka kusurwar ta kasance obtuse.

Trigonometric Properties na kusa da kusurwoyi

1. Zunubin kusurwoyi na kusa daidai suke, watau zunubi α = zunubi β.
2. Ma'auni na cosines da tangents na kusa da kusurwoyi daidai suke, amma suna da alamun sabani (sai dai ƙimar da ba a bayyana ba).
   • cos α = -kos β.
   • tg α = -tg β.