AVIATION MATHEMATICS AVIATION MATHEMATICS (GC_1)(GC_1)
COURSE OBJECTIVECOURSE OBJECTIVE
Students will get an overview of aviation Students will get an overview of aviation mathematics as permathematics as per– The requirement of regulatory bodiesThe requirement of regulatory bodies– The application of mathematical concepts The application of mathematical concepts
the fieldthe field
ALLOTTED TIME AND DELIVERYALLOTTED TIME AND DELIVERY
Duration Duration – 40 hours theory40 hours theory
DeliveryDelivery– Lecture discussionLecture discussion– Class exerciseClass exercise– Reading and class exercisesReading and class exercises– Home take exams/exercisesHome take exams/exercises
COURSE CONTENTCOURSE CONTENT
ArithmeticArithmetic Basic mathematical operation Basic mathematical operation
AlgebraAlgebra Linear, simultaneous and quadratic equationLinear, simultaneous and quadratic equation
GeometryGeometry An introductory viewAn introductory view
TrigonometryTrigonometry Practical problems on charts and graphsPractical problems on charts and graphs
TEXT BOOKS AND REFERENCESTEXT BOOKS AND REFERENCES
Ac – 65 – 9A, Airframe and Powerplant Ac – 65 – 9A, Airframe and Powerplant Series, General HandbookSeries, General Handbook
Technical Mathematics with CalculusTechnical Mathematics with Calculus Shop MathematicsShop Mathematics
EVALUATIONEVALUATION
Class testsClass tests AssignmentsAssignments Final testFinal test Passing markPassing mark
– 70%70%
DISCIPLINEDISCIPLINE
PunctualityPunctuality Good appearanceGood appearance I'D. cards in proper placeI'D. cards in proper place School regulationSchool regulation
ArithmeticArithmetic
ObjectiveObjective– Addition, subtraction, multiplication and Addition, subtraction, multiplication and
division of:division of: FractionsFractions DecimalsDecimals
– Conversion of Metric System to British Conversion of Metric System to British SystemSystem
– Calculation of ratio, average and percentageCalculation of ratio, average and percentage
Basic OperationsBasic Operations
Addition +Addition + Subtraction -Subtraction - Multiplication x () Multiplication x () ** Division Division ÷,/,÷,/, Grouping signsGrouping signs
TermsTerms
NumberNumber SumSum MinuendMinuend SubtrahendSubtrahend DifferenceDifference MultiplicandMultiplicand MultiplierMultiplier ProductProduct
Terms (Contd.)Terms (Contd.)
DividendDividend DivisorDivisor QuotientQuotient RemainderRemainder DigitsDigits DenominatorDenominator NumeratorNumerator
5 – 2 =3
7 x 3 = 21
27 / 5 = 5 and 2
Product
Quotient
Difference Subtrahend
Multiplier
Minuend
Multiplicand
Divisor
Dividend
Remainder
Number SystemNumber System
Counting NumbersCounting Numbers– { 1,2,3,4,…}{ 1,2,3,4,…}
Whole NumbersWhole Numbers– { 0,1,2,3,4,…}{ 0,1,2,3,4,…}
Integers (I)Integers (I)– {…,-3,-2,-1,0,1,2,3,…}{…,-3,-2,-1,0,1,2,3,…}
Rational Numbers Rational Numbers
Fractions Fractions
a/b , a a/b , a ЄЄ I, b I, b ЄЄ I I– Proper , a<b Proper , a<b 1/21/2– Improper, a>b Improper, a>b 4/34/3
– Mixed , a c/b Mixed , a c/b 33 2/3 2/3
Decimals , 0.5, 2.33, 4.1111…Decimals , 0.5, 2.33, 4.1111… Irrational numbers , 3.030030003…, Irrational numbers , 3.030030003…, ππ Real Numbers = R U IRReal Numbers = R U IR
Significant DigitsSignificant Digits
Measured dataMeasured data Reliability of a numberReliability of a number
– Precision Precision position of last reliable digitposition of last reliable digit– Accuracy Accuracy number of significant figure number of significant figure
E.g. 56.78, 0.0034, 5.600, 3.0080, 50,000E.g. 56.78, 0.0034, 5.600, 3.0080, 50,000 Rounding off a numberRounding off a number
– Even and odd caseEven and odd case
Rules Rules
Non-zero digits are always significant. Non-zero digits are always significant. Any zeros between two significant Any zeros between two significant
digits are significant. digits are significant. A final zero or trailing zeros in the A final zero or trailing zeros in the
decimal portion decimal portion ONLYONLY are significant. are significant. Round the final result to the least Round the final result to the least
number of significant figures of any one number of significant figures of any one term. term.
Multiples and FactorsMultiples and Factors
Factors Factors 27 : 1,3,9,2727 : 1,3,9,27
MultipleMultiple 3 : 3,6,9,12,…3 : 3,6,9,12,…
Prime factorsPrime factors 36 : 2,336 : 2,3
Greatest common factor (GCF)Greatest common factor (GCF) Least common multiple (LCM)Least common multiple (LCM)
Exercise Exercise
3 + 4 – 2 x 5 + 4 3 + 4 – 2 x 5 + 4 = =
5 + 1/100 + 7/1000 = 5 + 1/100 + 7/1000 = Change 3.333 to fractional formChange 3.333 to fractional form Change 4/3 to decimal formChange 4/3 to decimal form Go to drill for significant Go to drill for significant figuresfigures
Exercises (Cont.) Exercises (Cont.)
Round off the result of the following Round off the result of the following calculations to three significant digitscalculations to three significant digits
2.4x6.5x10.372.4x6.5x10.37 21.3x0.054/(97.4x3.80)21.3x0.054/(97.4x3.80)
Find the GCF of the followingFind the GCF of the following 10,15,3010,15,30 18,30,12,4218,30,12,42
Find the LCM of the followingFind the LCM of the following 3,4,53,4,5
Measurement Systems Measurement Systems
Metric system (SI)Metric system (SI)– MeterMeter– KilogramKilogram– secondsecond
British system (BS)British system (BS)– InchInch– PoundPound– Second Second
Comparison Comparison
Ratio : by dividing one number by anotherRatio : by dividing one number by another 15 to 3 15 to 3 15:3=15/3=5 15:3=15/3=5
Proportion : equality of two ratiosProportion : equality of two ratios a/b = c/d a/b = c/d 15:3::25:515:3::25:5
Variation : the result one when the other Variation : the result one when the other changeschanges– Direct Direct – Inverse Inverse
Percentage and AveragePercentage and Average
Percentage : by the hundredPercentage : by the hundred 2 = 200%, 1.5 = 150%2 = 200%, 1.5 = 150% 50 = 25% of 40050 = 25% of 400 15% of 60 = 915% of 60 = 9
Average : Average : – Average of 3,4,5,6,7 is (3+4+5+6+7)/5 = 5Average of 3,4,5,6,7 is (3+4+5+6+7)/5 = 5
RateRate– Division by timeDivision by time
Rate
Powers and RootsPowers and Roots
Power = root Power = root exponentexponent 9 = 39 = 322
Root = Root = indexindex√ Power√ Power 3 = 3 = 33√27√27
RulesRules– aaxx a ayy = a = a x+yx+y
– aaxx/a/ayy = a = ax-yx-y
– (a(axx))yy = a = axyxy
– 1/a1/axx = a = a-x-x
– xx√a = a√a = a1/x1/x
Logarithms Logarithms
100 = 10100 = 1022
– 2 is the logarithm of 100 on the base 102 is the logarithm of 100 on the base 10
Log(ab) = loga + logbLog(ab) = loga + logb Log(a/b) = log(a) – log(b) Log(a/b) = log(a) – log(b) Log(aLog(ab)b) = b = b**log(a)log(a)
43 x 69 = x 43 x 69 = x use logarithm tables to solve use logarithm tables to solve
Algebra Algebra
Objective : Objective : – To do algebraic operationsTo do algebraic operations– To solve linear equations, simultaneous To solve linear equations, simultaneous
equations, and quadratic equationsequations, and quadratic equations
Algebraic OperationAlgebraic Operation
Algebra : Relations and properties of Algebra : Relations and properties of numbers by means of letters, signs of numbers by means of letters, signs of operations and other symbols.operations and other symbols.
3x + 4y 3x + 4y
Expression
Coefficient
Term
Laws Laws
Associative lawAssociative law 3a + (2b – 3c) = (3a +2b) – 3c 3a + (2b – 3c) = (3a +2b) – 3c (a x b) x c = a x (b x c) (a x b) x c = a x (b x c)
Commutative lawCommutative law 3a x 2b = 2b x 3a3a x 2b = 2b x 3a
Distributive law Distributive law a(b + c) = ab + aca(b + c) = ab + ac
Special ProductsSpecial Products
(a + b) (a + b) = a(a + b) (a + b) = a22 +2ab + b +2ab + b2 2
(a - b) (a - b) = a(a - b) (a - b) = a22 - 2ab + b - 2ab + b22
(a + b) (a - b) = a(a + b) (a - b) = a22 - b - b22
(a + b) (a + ) = a(a + b) (a + ) = a22 +a(b + c) + bc +a(b + c) + bc (a + b) (c + d) = ac + ad + bc + bd(a + b) (c + d) = ac + ad + bc + bd aa33 + b + b33= (a + b) (a= (a + b) (a22 - ab + b - ab + b2)2)
aa33 - b - b33= (a - b) (a= (a - b) (a22 + ab + b + ab + b2)2)
Simplification of ExpressionsSimplification of Expressions
Exercises Exercises
Equations Equations
Linear equationsLinear equations3x + 5 = 9x – 73x + 5 = 9x – 7
Word problemsWord problems Simultaneous equationsSimultaneous equations
Algebraic sentence
Quadratic EquationsQuadratic Equations
axax22 + bx + c = 0 + bx + c = 0 SolutionsSolutions
– By plotting graphsBy plotting graphs– By completing the squareBy completing the square– By quadratic formulaBy quadratic formula
a
acbbx
2
42
Geometry Geometry
Objective : Objective : – To evaluate the areas and volumes of different To evaluate the areas and volumes of different
geometric shapes.geometric shapes.– To understand the relationship of angular, linear To understand the relationship of angular, linear
and irregular geometric figures.and irregular geometric figures.
Area And VolumeArea And Volume
A = BH
A = BH
A = BH/2
A = πR2
V = πR2H
V = BHD
V = πR2H/3
V = 4πR3/3
A = 4πR2
Fundamental ConceptsFundamental Concepts
Point Point
– Designation Designation .., + , x, , + , x, ○○
Line Line – One dimensionalOne dimensional– Path traced by a pointPath traced by a point– Types Types
SegmentSegment StraightStraight curvedcurved
Plane Plane – Two dimensionalTwo dimensional– Path traced by a linePath traced by a line
Volume Volume – Three dimensionalThree dimensional– Path traced by surfacesPath traced by surfaces
Fundamental Concepts (Contd.)Fundamental Concepts (Contd.)
Angles Angles Made by two straight lines which are Made by two straight lines which are
intersectingintersecting– AcuteAcute– ObtuseObtuse– Right Right
MeasurementMeasurement– DegreeDegree– RadianRadian– GradientGradient– Revolutions Revolutions
Triangles Triangles
Right Right
Isosceles Isosceles
Equilateral Equilateral
ScaleneScalene
Polygons Polygons
SquareSquare
PentagonPentagon
HexagonHexagon
Heptagon …Heptagon …
Circles and ArcsCircles and Arcs
Area = Area = ππrr22 ,perimeter = 2 ,perimeter = 2ππr r
ArithmeticsArithmetics 3939
H
B A = 1/2 BH
AREAAREA
1. TRIANGLE
ArithmeticsArithmetics 4040
S
S
A = S2
B. RECTANGLE
B2
AREAAREA
H
B1
2. QUADRILATERALA. SQUARE
H
B
A = BH
H
B
A = BHA.TRAPEZOID
A = 1/2 ( B1 + B2) H
C. PARALLELOGRAM
ArithmeticsArithmetics 4141
AREAAREA
R
CIRCLE
A = R2 A = R2 360
SECTOR
ArithmeticsArithmetics 4242
VOLUMEVOLUME
H
W
L
S
SS
HR
CUBE RECTANGULAR BLOCK
CIRCULAR CYLINDER
V = R2HV = HLWV = S3
ArithmeticsArithmetics 4343
VOLUMEVOLUME
H
R
R
H R
CONEFRUSTUM OF A CONE SPHERE
V = 1 R2 H 3
V = 1 H(R12 +R2
2+R1R2 ) 3
V = 4 R3 3
ALGEBRAALGEBRA
EXPRESSEXPRESS ANALYZEANALYZE
EG. EG.
POWER = F ( FUEL, RPM) POWER = F ( FUEL, RPM)
ALGEBRAIC EXPRESSIONALGEBRAIC EXPRESSION
3A = 3 X A3A = 3 X A 5B + 2C = 5 X B + 2 X C5B + 2C = 5 X B + 2 X C
TERMTERM: PARTS OF EXPRESSION CONNECTED BY : PARTS OF EXPRESSION CONNECTED BY ADDITION.ADDITION.
EG. EG. 6X6X + + 5Y5Y 6X AND 5Y ARE TERMS OF THE EXPRESSION6X AND 5Y ARE TERMS OF THE EXPRESSION
COEFFICIENTCOEFFICIENT: NUMERICAL PART OF A TERM.: NUMERICAL PART OF A TERM.EG. EG. 66X + X + 55YY 6 & 5 ARE COEFFICIENTS.6 & 5 ARE COEFFICIENTS.
RULES OF ALGEBRAIC RULES OF ALGEBRAIC EXPRESSIONEXPRESSION
1. ASSOCIATIVE LAW1. ASSOCIATIVE LAW– 2C + 4D + 3F = (2C + 4D) + 3F2C + 4D + 3F = (2C + 4D) + 3F
= 2C + (4D + 3F)= 2C + (4D + 3F)
– 2C X 4D X 3F = 2C X (4D X 3F)2C X 4D X 3F = 2C X (4D X 3F) = (2C X 4D) X 3F= (2C X 4D) X 3F = 24CDF= 24CDF
2. COMMUTATIVE LAW2. COMMUTATIVE LAW– 2C + 4D = 4D + 2C2C + 4D = 4D + 2C
– 2C X 4D = 4D X 2C = 4CD2C X 4D = 4D X 2C = 4CD
RULES OF ALGEBRAIC RULES OF ALGEBRAIC EXPRESSIONEXPRESSION
3. DISTRIBUTIVE LAW3. DISTRIBUTIVE LAW– 2 (3 + 4) = 2X3 + 2X4 = 142 (3 + 4) = 2X3 + 2X4 = 14– A ( B + C ) = AB + ACA ( B + C ) = AB + AC– (A + B) / C = A / C + B / C(A + B) / C = A / C + B / C– A ( B - C ) = AB - ACA ( B - C ) = AB - AC– (A - B) / C = A / C - B / C(A - B) / C = A / C - B / C
ALGEBRAIC ADDITIONALGEBRAIC ADDITION
LIKE TERMSLIKE TERMS: TERMS THAT HAVE THE SAME : TERMS THAT HAVE THE SAME SYMBOLIC PART.SYMBOLIC PART.
TO ADD:TO ADD:– COLLECT LIKE TERMSCOLLECT LIKE TERMS– ADD COEFFICIENTADD COEFFICIENT
Eg. Eg. 3A + 5A + 9A = (3 + 5 + 9)A3A + 5A + 9A = (3 + 5 + 9)A
= = 17A17A
ALGEBRAIC MULTIPLICATIONALGEBRAIC MULTIPLICATION
FACTORS: FACTORS: PARTS OR ELEMENT PARTS OR ELEMENT SYMBOLS OPERATED BY SYMBOLS OPERATED BY MULTIPLICATION.MULTIPLICATION.
TO MULTIPLY:TO MULTIPLY:– COLLECT FACTORSCOLLECT FACTORS
EG. 2 X B X C = 2BCEG. 2 X B X C = 2BC
CONVENTIONCONVENTION
BODMASBODMAS = ( BRACKET OF DIVISION, = ( BRACKET OF DIVISION, MULTIPLICATION, ADDITION, AND MULTIPLICATION, ADDITION, AND SUBTRACTION)SUBTRACTION)
EG. EG. – A + B X C = A + BCA + B X C = A + BC– (A + B) X C = AC + BC(A + B) X C = AC + BC
SYMBOLS OF GROUPINGSYMBOLS OF GROUPING– ( ) , [ ] , { }( ) , [ ] , { }
1. a1. ann = a. a. a. … . a (to n factors of “a”) = a. a. a. … . a (to n factors of “a”) 2 a2 amm . a . ann = a = am+nm+n
(a (a mm))nn = a = amnmn
(ab)(ab)nn = a = ann.b.bnn
(a/b)(a/b)nn = a = ann/b/bnn
(1/b)(1/b)nn= 1/b= 1/bn n =b=b-n-n
aamm/a/an n = a= a(m-n)(m-n)
- - - - - {If n is even (any - - - - - {If n is even (any integer) integer) then a>o if n is odd then a>o if n is odd then athen aR.}R.}
aa00 = 1, a = 1, a00
Rules of ExponentRules of Exponent
nn aa /1
Special Products and FactorsSpecial Products and Factors
aa22 - b - b22 = (a + b) (a – b) = (a + b) (a – b) aa22+2ab+b+2ab+b22 = (a+b) (a+b) = (a+b) = (a+b) (a+b) = (a+b)22
aa22– 2ab + b– 2ab + b22 = (a-b) (a–b) = (a- b) = (a-b) (a–b) = (a- b)22
aa33 – b – b33 = (a- b) (a = (a- b) (a22 + ab + b + ab + b22)) aa33 + b + b33 = (a+b) (a = (a+b) (a22 – ab + b – ab + b22))
EquationEquation
Expression related to each other by an equality sign (=) Expression related to each other by an equality sign (=) Eg. 2x2 + 4x +3 = 7x + 5Eg. 2x2 + 4x +3 = 7x + 5 x+5y =2y+3xx+5y =2y+3x
Solving Linear EquationSolving Linear Equation Add or subtract the same number on both sides to Add or subtract the same number on both sides to
collect the same terms to one side.collect the same terms to one side. Multiply or divide both sides by the same number to Multiply or divide both sides by the same number to
solve for the variable.solve for the variable.Eg. 3x + 5 = 2x + 7Eg. 3x + 5 = 2x + 7Step 3x + 5 – 5 = 2x + 7 – 5Step 3x + 5 – 5 = 2x + 7 – 5 3x = 2x + 23x = 2x + 2 3x – 2x = 2x – 2x + 23x – 2x = 2x – 2x + 2 x = 2x = 2
Quadratic EquationQuadratic Equation
These are equation of second order.These are equation of second order.
Quadratic equation in one variable.Quadratic equation in one variable.3x3x22 + 5x + 2 = 0 + 5x + 2 = 0 axax22 + bx + c = 0 , + bx + c = 0 , aa00
Quadratic equation in two variable Quadratic equation in two variable axax22 + bx +c + dy + bx +c + dy22 + ey + f = 0 + ey + f = 0
Where a, b, c, d, e, and f are constants. a and d are Where a, b, c, d, e, and f are constants. a and d are different from zero.different from zero.
Consider:Consider:axax22 + bx + c = 0 , + bx + c = 0 , aa00
Case 1: When b = 0Case 1: When b = 0 axax22 + C = 0 + C = 0Solving for xSolving for x xx22 = = -c -c aa
Solving Quadratic EquationSolving Quadratic Equation
)(a
cx
,
0a
c
Case 2: When c = 0Case 2: When c = 0
axax22 + bx = 0 + bx = 0
Solving for x:Solving for x:
axax22 + bx = 0 + bx = 0
x (ax + b ) = 0x (ax + b ) = 0
x = 0x = 0 or ax + b = 0 or ax + b = 0
ax = -bax = -b
x = -b/ax = -b/a
Case 3:Case 3: a, b ,and c a, b ,and c 0 0
Eqn. axEqn. ax22 + bx + c = 0 + bx + c = 0
This can be solved by one of the following.This can be solved by one of the following. Plotting ( inaccurate) **Plotting ( inaccurate) ** FactorizationFactorization Completing the squareCompleting the square Quadratic formulaQuadratic formula
Quadratic Formula:
. . . .. . . . . . 2
42
a
acbbX
,
042 acb
Simultaneous EquationsSimultaneous Equations
Linear simultaneous equation can be solved byLinear simultaneous equation can be solved by Graphical method (approximate)Graphical method (approximate) Algebraic methodAlgebraic method
– Elimination Elimination – Substitution (*)Substitution (*)
Eg. Eg. 2x + 4y = 5 (1)2x + 4y = 5 (1)
x + y = 3 (2)x + y = 3 (2)
GeometryGeometry 5959
GEOMETRYGEOMETRYFundamentals of geometry1. Point .
2. Line
3. Straight line
4. Line Segment
5. Half Straight line
6. Parallel line
GeometryGeometry 6060
Complementary Angles
Suplementary angles
Adjacent Angles
Equilateral Triangle
Isosceles Triangle
Right Angle Triangle
• Oblique Angle Triangle
GeometryGeometry 6161
7. Angle
a) Straight angle
b) Obtuse
c) Right angle
d) Acute
GeometryGeometry 6262
Square
Rectangle
Parallelogram
Rhombus
Chord
Sector
Segment
Tangent to Circle
Quadrilateral Circle
GeometryGeometry 6363
RulesRules
1. Opposite or vertical angles are equal.
2. Alternate interior angles are equal.
GeometryGeometry 6464
RulesRules
3. Corresponding angles are equal.
4. The sum of the interior angles of a triangle is always 180.
GeometryGeometry 6565
RulesRules
A
D
BCF E
D
F E
A
BC
5. Two triangles are similar when their corresponding angles are equal.Corresponding sides of similar triangles are proportional
6. Two triangles are congruentI. SASII. ASAIII. SSS
GeometryGeometry 6666
RulesRules
7. Pythagoras Theorem
8. The sum of the interior angles of a convex poly gon with n-sides is = (2n – 4)rts. = 180(n - 2)
a c
b
a2 + b2 = c2
GeometryGeometry 6767
RulesRules
A B
CD
k
9. The sum of the exterior angles of a convex polygon with n sides is = 4 rts (360o).
10. If ABCD is a parallelogramI. AB = CD and AD =BC;II. A = C and B = D;III. BD bisect area ABCD.IV. AK = KC and BK = KD
GeometryGeometry 6868
11. Condition for a quadrilateral to be a parallelogramI. AB is equal and parallel to DC,II. A=C and B = DIII. If AB = DC and AD =BCIV. If AK = KC and BK=KD
12. TriangleI.11. If in ABC, AC > AB then B > C.II.If in ABC, B > C then AC > AB .III.If ABC is any triangle, AB + AC > BC
A
B C
A B
CD
k
GeometryGeometry 6969
RulesRules
B C
H K
A
N PA B
13. If CN is the perpendicular from C to a straight line AB and NP then CN < CP
14. If H, K are the mid-points of AB, AC respectively, thenHK is Parallel to BCHK = BC / 2
GeometryGeometry 7070
RulesRules
-The altitudes of a triangle are concurrent.The point is orthocentre or the triangle.
A
C
B
D
Pwere
Q
R
S
E T
15. If two transversals ABCDE, PQRST are cut by the parallel lines BQ, CR, DS, ET, and if BC=CD=DE then QR = RS = ST.
16. The medians AD, BE, CF of ABC concur at a point G, such thatDG = 1/3DAEG = 1/3 EBFG = 1/3FG
A
B
C
D
E
F
G
GeometryGeometry 7171
RulesRules
17. The perpendicular bisectors of the three sides of a triangle are concurrent. The point at which they concur is the circum-center of the triangle
18.The altitudes of a triangle are concurrent
The point is called ortho-center of the triangle
GeometryGeometry 7272
RulesRules
19.The internal bisectors of the three angles of a triangle are concurrent.
The point at which they concur is called the in-center of the triangle
GeometryGeometry 7373
RulesRules
CircleIf M is the mid-point of a chord AB of a circle, center o, then < OMA = 1rt <
If the chords AB and CD of a circle are equal, they are equidistant from the centre.
If the chords AB and CD of a circle equidistance from the centre, then AB = CD
D
C
A
Bx
OM
GeometryGeometry 7474
RulesRules
There is one circle, and only one circle that pass through There is one circle, and only one circle that pass through three given points A, B, C not in the same straight line.three given points A, B, C not in the same straight line.
The perpendicular bisectors of AB , BC, and CA meet at The perpendicular bisectors of AB , BC, and CA meet at the centre 0 of the circle.the centre 0 of the circle.
The angle which an arc of a circle subtends at the center The angle which an arc of a circle subtends at the center is double that which subtends at any point on the is double that which subtends at any point on the remaining part of the circumference remaining part of the circumference
<AOB = 2 x <ACB<AOB = 2 x <ACB
x
A
B
C
O
The end.The end.
Trigonometry Trigonometry
Sine Sine α = A/C = A/C cosine cosine α = B/C = B/C Tangent Tangent α = B/A = B/A
C
A
B
α
Charts & GraphsCharts & Graphs