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Ja es tev pieietu uz ielas un pajautātu –

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tik treknā šriftā negribēju rakstīt –

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saki, lūdzu, cik ir sīnuss
no pī dalīts ar 4, –

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un mēs, protams, runājam par vērtību radiānos –

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tu to būsi vai nu iemācījies no galvas,

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vai uzzīmēsi vienības riņķi,
lai atrastu atbildi.

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Nav pats skaistākais vienības riņķis,
bet priekšstatam derēs.

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Tu atliktu leņķi ar platumu
pī dalīts ar 4 radiāni,

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kas ir tas pats, kas 45 grādu leņķis.

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Atbilstošajā riņķa vietā
tu novilktu rādiusu.

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Un sinuss ir šī punkta y koordināta
vienības riņķī.

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Tātad mēs gribam noskaidrot šo te vērtību.

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Mums tātad ir dots,
ka šis ir 45 grādu leņķis.

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Pārzīmēšu šo trijstūri mazliet lielāku.

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Trijstūris izskatās šādi.

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Šis ir 45 grādu leņķis,

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tas ir 45 grādu leņķis,

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un šeit ir 90 grādi.

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Nu varam vajadzīgo aprēķināt
45, 45 un 90 grādu trijstūrī.

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Hipotenūza ir 1 vienību gara.

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Šī mala ir x. Šī mala ir x.

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Abas malas ir vienāda garuma,
jo šis ir vienādsānu trijstūris.

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Leņķi pie pamata ir vienādi.

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Tātad x kvadrātā plus x kvadrātā

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ir vienāds ar 1 kvadrātā, kas ir 1.

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2 x kvadrātā ir vienāds ar 1;

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x kvadrātā ir vienāds ar 1/2.

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X ir vienāds ar kvadrāsakni no 1/2,

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un tas ir 1 dalīts ar kvadrātsakni no 2.

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Varam to izteikt racionālā formā,

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skaitītāju un saucēju pareizinot
ar kvadrātsakni no 2
dalīts ar kvadrātsakni no 2.

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Iegūstam, ka x ir vienāds
ar kvadrātsakni no 2 dalīts ar 2.

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Tātad šis augstums ir
kvadrātsakne no 2 dalīts ar 2.

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Un tikpat garš būs arī šis attālums.

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Taču mums vajag tikai augstumu,

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jo sinusa vērtība, šī leņķa sinuss,

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atbilst šim augstumam – y koordinātai.

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Un mēs noskaidrojām,
ka tas ir kvadrātsakne no 2 dalīts ar 2.

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Šis viss ir atkārtojums –

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mēs to apguvām vienības riņķa video.

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Bet ja nu kādu citu dienu
pienāktu tev klāt un pajautātu:

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"Saki, lūdzu, –

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saki, lūdzu, cik ir arksinuss
no kvadrātsaknes no 2 dalīts ar 2?"

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Kas ir arksinuss?

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Tu, iespējams, apjuktu –
tu zini, kas ir leņķa sinuss,

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bet te Salmans runā par kaut kādu
jaunu trigonometrisko funkciju.

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Taču patiesībā vienīgais, kas jāzina,
ja vārda sākumā ir šī "ark" daļa...

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to reizēm dēvē arī par INVERSO
JEB APGRIEZTO SINUSU.

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To varētu pierakstīt arī šādi:

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kāds ir INVERSAIS sinuss
no kvadrātsaknes no 2 dalīts ar 2?

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Būtībā tiek jautāts,
kādam leņķim jānosaka sinuss,

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lai iegūtā vērtība būtu
kvadrātsakne no 2 dalīts ar 2.

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Tātad tiek jautāts,
kādam leņķim jānosaka sinuss,

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lai iegūtu kvadrātsakni no 2 dalīts ar 2.

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