Sin vs Cos
Cov ceg ntawm kev ua lej, uas cuam tshuam nrog ob sab thiab lub kaum sab xis ntawm daim duab peb sab thiab trigonometric ua haujlwm ntawm cov ces kaum yog hu ua trigonometry. Lub hauv paus trigonometric functions ntawm lub kaum sab xis yog sine (kev txhaum) thiab cosine (cos) ntawm lub kaum sab xis. Trigonometric sin thiab cos yog qhov sib piv ntawm ob sab tshwj xeeb hauv lub kaum sab xis daim duab peb sab thiab muaj txiaj ntsig zoo hauv kev cuam tshuam cov kaum sab xis thiab sab ntawm daim duab peb sab. Kev siv cov kev txhaum trigonometric thiab cos tau nce sai hauv kev daws teeb meem engineering, navigation thiab physics.
Sine (Sin)
Sine yog thawj txoj haujlwm trigonometric. Trigonometric Sine yog siv los xam qhov "nce" ntawm ib kab segment nrog rau kab rov tav kab hauv ib daim duab peb sab. Rau lub kaum sab xis ntawm lub kaum sab xis, sine ntawm lub kaum sab xis yog qhov piv ntawm qhov ntev ntawm perpendicular los yog opposite sab rau hypotenuse. Nws yog qhia nyob rau hauv cov nqe lus ntawm sine θ, qhov twg θ yog lub kaum sab xis ntawm opposite sab thiab hypotenuse. Sine θ yog abbreviated li sin θ. Hais txog kev hais lus
Sin θ=opposite sab ntawm daim duab peb sab / hypotenuse ntawm daim duab peb sab.
Trigonometric sine yog siv los kawm txog lub sijhawm ntawm lub suab thiab lub teeb nthwv dej, txiav txim siab qhov ntsuas kub nruab nrab ntawm txhua lub xyoo, suav hnub ntev, txoj haujlwm ntawm kev sib haum xeeb oscillators thiab ntau ntxiv. Lub inverse ntawm sine θ yog cosecant θ. Cosecant θ yog qhov piv ntawm hypotenuse rau sab nraud ntawm daim duab peb sab thiab abbreviated li Cosec θ.
Cosine (Cos)
Cosine yog qhov thib ob trigonometric muaj nuj nqi. Nrog rau kev hwm ntawm kab kab rov tav, cosine yog siv los xam "khiav" ntawm lub kaum sab xis. Rau lub kaum sab xis ntawm daim duab peb sab, cosine ntawm lub kaum sab xis yog qhov piv ntawm lub hauv paus lossis sab uas nyob ib sab rau hypotenuse ntawm daim duab peb sab. Lo lus no tau qhia tias yog cosine θ, qhov twg θ yog lub kaum sab xis ntawm sab thiab hypotenuse. Cosine θ yog abbreviated li Cos θ. Hais txog kev hais lus
Cos θ=ib sab ntawm daim duab peb sab / hypotenuse ntawm daim duab peb sab
Tus inverse ntawm Cos θ yog secant θ. Secant θ yog qhov piv ntawm hypotenuse rau ib sab ntawm daim duab peb sab. Secant θ yog abbreviated li Sec θ.
Kev sib piv
• Yog hais tias qhov ntev ntawm ib txoj kab yog 1 cm, sine qhia qhov nce nrog kev hwm rau lub kaum sab xis, thaum rau tib qhov ntev ntawm kab, Cos qhia kev khiav ntawm lub kaum ntse ntse.
• Txoj Cai ntawm Sine yog siv los xam qhov ntev ntawm sab tsis paub ntawm daim duab peb sab, uas nws ib sab thiab ob lub kaum sab xis paub. Whereas txoj cai ntawm Cosine yog siv los xam cov sab ntawm daim duab peb sab, uas nws lub kaum sab xis thiab ob sab paub.
• Raws li 2 π radian=360 degree, yog li yog tias peb xav suav cov txiaj ntsig ntawm Sin thiab Cos rau lub kaum siab dua 2 π lossis tsawg dua -2 π, ces Kev txhaum thiab Cosine yog lub sijhawm ua haujlwm ntawm 2 π. Like
Sin θ=Sin (θ + 2 π k)
Cos θ=Cos (θ + 2 π k)
Zaj lus
Sine thiab cosine yog thawj txoj haujlwm trigonometric; Txawm li cas los xij, txhua txoj haujlwm muaj nws qhov tseem ceeb hauv kev daws teeb meem kev ua lej. Txawm li cas los xij, Yog tias peb nthuav qhia sine thiab cosine nyob rau hauv lub sij hawm ntawm radian, peb tuaj yeem sib cuam tshuam ob lub trigonometric identities nyob rau hauv cov nqe lus ntawm radian yog
Sin θ=Cos (π/2 – θ) and Cos θ=Sin (π/2 – θ)
