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8/2/2019 BTEC NC - Maths - Trigonometry
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Brendan Burr BTEC National Certificate in ElectronicsTrigonometric Methods
1
8/2/2019 BTEC NC - Maths - Trigonometry
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Brendan Burr BTEC National Certificate in ElectronicsTrigonometric Methods
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8/2/2019 BTEC NC - Maths - Trigonometry
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Brendan Burr BTEC National Certificate in ElectronicsTrigonometric Methods
Task 1
1.1
BAD = 53ºAB = 2.44mABD = 180 – (53 + 90)
= 37ºBCD = 41ºCBD = 180 – (41 + 90)
= 49ºBD = Sin(53) = opp
2.44
= Sin(53) x 2.44 = opp
= 1.95m
AD = 2.44² - 1.95²= 2.1511m= 1.47m (Square Root)
BC = opp = hypSin(41)
= 1.95 = 2.97m
Sin(41)
CD = 2.97² - 1.95²= 5.0184m= 2.24m (Square Root)
AC = 1.47 + 2.24= 3.71m
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Brendan Burr BTEC National Certificate in ElectronicsTrigonometric Methods
1.2
The height of the tower = BC + 1.5m
BC = Tan 30 x Adj= Tan 30 x 100= 57.74m
Height of the tower
= 57.74 + 1.5= 59.24m
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Arc
θ
r
Brendan Burr BTEC National Certificate in ElectronicsTrigonometric Methods
1.3
r = 200mmθ = 2л radians
3
a) Calculate the length of the arc:
θ = 2л radians3
= 120º
θ x Circumference360
Circumference = 2 rл= 1256.66mm
Arc = 200 x 2 . л3
= 418.89mm
b) Calculate the area sector:
Area = r²л
= x 200²л
= 125663.7061mm²
Area of sector= 1 x 2002 x 2 x л
2 3= 41887.90205mm²
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Brendan Burr BTEC National Certificate in ElectronicsTrigonometric Methods
3.1a)
Calculate the values of thetriangle above, using the sine rule.
Sine Rule = __ a__ = __b__ = __c__ Sin A Sin B Sin C
= __a__ = __c__
Sin A Sin C
= __a__x__Sin C__ = cSin A
= 42.5 x Sin(105) = cSin(43)
AB = 60.19346969mm
AC = __b__ = __c__ Sin B Sin C
= __c__x__Sin B__ = cSin C
= 60.19346969 x Sin(32)Sin(105)
AC = 33.02290745mm
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Brendan Burr BTEC National Certificate in ElectronicsTrigonometric Methods
3.2
Cosine Rule =a² = b² + c² - 2bc Cos A
b² = a² + c² - 2ac Cos Bc² = a² + b² - 2ab Cos C
= b² = 2.4² + 3² - (2 x (2.4 x 3)) x Cos 125= 23.01950068m= 4.797864179m (Square Root)
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Brendan Burr BTEC National Certificate in ElectronicsTrigonometric Methods
Bibliography
Through guidance from my lecturer, the following websites and textbooks I was able to complete this assignment:
BooksBTEC National Engineering (Mike Tooley & Lloyd Dingle)ISBN: 978-0-7506-8521-4Higher Engineering Mathematics (John Bird)ISBN: 978-0-7506-8152-0
Websiteswww.wikipedia.org
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