Findtheexactvalueofcos75°
Findingthevalueof couldbeachievedbylookingup trigonometrictableorsimplycalculatingusingvariouscalculator.An approximatedecimalvalueisgivensincetheexactvalueof is anirrationalnumber.
Approximatevalueofcos75°
Oncethevalueof isavailable,it'seasytoobtainthevalueof usingthetrigonometricco-functionidentity. Sincetherearetwounitsusedforanglemeasurement,degreeand radian, couldalsobeexpressedinradiansangle.
Aquestionmayarise,howdoestheapproximatevaluecomeout?Isit possibletoderivetheexactvalueof ?
Well,sinceisamultipleof, couldbederivedbyusing trigonometricidentitiesandvaluesofspecialangles. Normallytherearemorethanonewaytoderivethetrigonometric valueofaspecialangle.Theexactvalueof couldbe determinedbythetrigonometricvaluesofandusingsum identityforcosinefunction.Sinceishalfof, could alsobederivedbyusinghalfangleidentity.
Usingsumidentityforcosinefunction
Thesumidentityforcosinefunctioncouldtransformatrigonometric functionofanangletothedifferenceofproductsofcosinefunctions oftwoanglesandproductsofsinesfunctionsoftwoanglesthatare addeduptotheoriginalangle. Theexactvalueof couldbedeterminedbythetrigonometric valuesofandusingsumidentityforcosinefunction.
Thetrigonometricvaluesofspecialangleswearegoingtouseare listedinthetablebelow.
Theexactvaluesfor and couldbedeterminedwith thehelpof30-60-90rightangletriangle.Theexactvaluesof and couldbederivedgeometricallywiththehelpofisosceles righttriangle.
Itshouldbenotedthatmostofthetrigonometricvaluesofthese specialanglesareirrationalnumbers.Soitisexpectedthesamefor thevaluesthatareresultedinbyoperationofthesenumbers.
Nowlet'ssubstitutespecialanglesandtheirtrigonometricvaluesto theidentity(1)
Collectedintheboard:TrigonometricValuesofSpecialAngles
StevenZhengposted4monthsago
©2021MathSolution.AllRightsReserved.PrivacyPolicy
