Magirafu eMabasa eTrigonometric
Mabasa eTrigonometric, anobva muhukama huripo pakati pemakona nemativi etriangles, akakosha mu masvomhu, sainzi, uye engineering. Mabasa aya—sine (sin), cosine (cos), tangent (tan), cosecant (csc), secant (sec), uye cotangent (cot)—anogara kwenguva refu, zvichireva kuti anodzokorora kukosha kwawo nguva nenguva. Kunzwisisa magirafu avo kwakakosha pamashandisirwo akawanda, kubva pakugadzirisa masaini kusvika pakudzidza zviitiko zvenguva pfupi muzvisikwa.
1. Mabasa eChikamu cheChikamu neTrigonometric
Mashandiro etrigonometric anogona kuratidzwa uchishandisa denderedzwa reyuniti—denderedzwa reradius rakanangana nekwakabva denderedzwa reyuniti. Angle θ, inoyerwa mumaradians, inotsvairwa kubva pa x-axis yakanaka. Ma coordinates (x, y) enzvimbo iyo divi rekupedzisira rekona rinosangana nedenderedzwa reyuniti anopa ruzivo rwakakosha:
– x = cos(θ)
– y = chivi(θ)
2. Kugadzira Mifananidzo yeSine neCosine Mabasa
Mabasa eSine neCosine, akakosha muTrigonometry, anosiyaniswa nemapatani awo akasiyana akafanana nemafungu.
Basa reSine
Girafu ye y = sin(θ) inotanga pamavambo (0,0) uye inotevera wave yakatsetseka, inoenderera mberi:
– Nguva: Nguva yekutenderera kamwe chete kwekushanda kwesine i2π. Izvi zvinoreva kuti y = sin(θ) inodzokorora radians yega yega ye2π.
– Amplitude: Huwandu hwepamusoro nehwepasi hwe sin(θ) ndi1 na -1, zvichiteerana.
– Pfungwa Huru: Pfungwa dzakakosha pagirafu dzinosanganisira (0,0), (π/2,1), (π,0), (3π/2,-1), uye (2π,0).
Pamifananidzo, sine wave inotenderera zvakanaka pakati pe -1 ne 1, ichiyambuka x-axis pahuwandu hwe π uye ichisvika pahuwandu hwayo hwepamusoro uye hwepasi pahuwandu hwe odd hwe π/2.
Basa reCosine
Basa re cosine y = cos(θ) rine kufanana nebasa re sine asi rinoshanduka rakatwasuka:
– Nguva: Kufanana nebasa resine, basa recosine rine nguva ye2π.
– Amplitude: Huwandu hwezvinhu zve cos(θ) hunobvawo pa -1 kusvika pa 1.
– Pfungwa Huru: Pfungwa dzinonyanya kukosha pagirafu dzinosanganisira (0,1), (π/2,0), (π,-1), (3π/2,0), uye (2π,1).
Panyaya yekuonekwa, cosine wave inotanga nehukuru hwayo hwepamusoro hwe1. Patani yemafungu inoratidza periodicity yakapfava uye amplitude yakafanana nekushanda kwesine asi yakachinjirwa kuruboshwe ne π/2 radians.
3. Kugadzira Magirafu eTangent neCotangent Mabasa
Basa reTangent
Girafu ye y = tan(θ) inomiririra chiyero che sine ne cosine:
– Nguva: Nguva yekutenderera kamwe chete kwakazara kwebasa retangent i π.
– Zvisina kujeka: Tangent haina kutsanangurwa apo cos(θ) = 0, zvichikonzera kuti zvisina kujeka zvakamira paθ = (n+1/2)π apo n iri nhamba yese.
– Pfungwa huru: Pfungwa dzinokosha dzinosanganisira (0,0), (π/4,1), uye (-π/4,-1).
Girafu yetangent inopfuura nepakabva uye inowedzera isina kusungwa painosvika paasymptotes, zvichigadzira macurve akatevedzana akafanana neakawanda emahyperbolas.
Basa reCotangent
Iyo cotangent basa y = rukukwe(θ) = cos(θ)/chivi(θ) inoratidza maitiro akasiyana:
– Nguva: Nguva ye cotangent i π.
– Zvisina Kujeka: Cotangent haina kutsanangurwa apo sin(θ) = 0, zvichikonzera kuti pave nezviratidzo zvakamira pazviverengero zveπ.
– Pfungwa Huru: Hunhu hunosanganisira θ = (π/4,1), (3π/4,-1), nezvimwewo.
Nekudhirowa cotangent, tinoona ma curves anoenderera mberi akafanana nee tangent asi akaenzaniswa uye akaratidzwa nekuda kwehunhu hwemabasa ekudzokorora.
4. Kugadzira Mifananidzo yeCosecant neSecant Functions
Basa reCosecant
Basa rekuti y = csc(θ) = 1/sin(θ) rinounza zvirevo zvakafanana:
– MaAsymptotes: Basa recosecant rine maasymptotes akamira apo sin(θ) = 0, zvichiitika pahuwandu hweπ.
– Maitiro: Sezvo y = csc(θ) iri kudzokorora kwe y = sin(θ), kana sin(θ) iri diki kwazvo, csc(θ) inova yakakura zvikuru, uye zvinopesana.
Girafu yecosecant inoratidzwa nematanho akatevedzana anosvika pakusingaperi pedyo neasymptotes, zvichigadzira patani yemaumbirwo eparabolic akabatana pakati peasymptotes.
Basa reSecant
Saizvozvowo, y = sec(θ) = 1/cos(θ) inoratidzwa senzira yekubatanidza basa re cosine:
– Zvisina Mwero: Izvi zvinoitika panzvimbo apo cos(θ) = 0, ndiko kuti, apo θ = (2n+1)π/2.
– Maitiro: Girafu inoratidza kukosha kukuru pedyo neasymptotes dzakamira uye kukosha kudiki pakati padzo.
Girafu inobuda ye secant ine mapazi e parabolic akatarisana ne cosine graph, ichiratidza hukama hwakaoma pakati pemabasa e reciprocal trigonometric nemabasa avo emubereki.
5. Kuchinja
Mabasa eTrigonometric anogona kuchinjwa, kutambanudza, uye kuratidzwa nekushandura maequation avo ekutanga:
– Kuchinja Kwakatsetseka: Kuwedzera chinoramba chiripo, sezviri muna y = sin(θ) + c, kunofambisa girafu kumusoro kana pasi nemayuniti e c.
– Kuchinja Kwakatambanuka: Kuwedzera/kubvisa mukati mebasa, sezviri mu y = sin(θ – d), kunoshandura girafu kuruboshwe kana kurudyi.
– Amplitude: Kukwidza basa, semuenzaniso, y = a sin(θ), kunochinja kukwirira kwemakomo nemipata.
– Kugadziriswa kwePeriod: Kuchinja frequency, semuenzaniso, y = sin(bθ), kunokanganisa huwandu hwema cycles muchikamu chakapihwa. Semuenzaniso, y = sin(2θ) inogadzira wave ine hafu yenguva ye sine wave yekutanga.
mhedziso
Magirafu emabasa etrigonometric anopa zvishandiso zvine simba zvekuona kuti unzwisise zviitiko zvenguva nenguva. Kugona magirafu aya kunosanganisira kuziva mapatani ekutanga esine, cosine, tangent, uye zvinodzokororwa, pamwe nekunzwisisa shanduko dzinogadzirisa chimiro chavo nenzvimbo. Nekushandisa kunosanganisira madhigirii akasiyana-siyana, kunzwisisa kwakakwana kwemifananidzo iyi kunoisa hwaro hwakakosha hwekudzidza kwepamusoro uye kuita mabasa munzvimbo dzakasiyana-siyana dzakadai sefizikisi, mainjiniya, nezvimwe.
