MATHS PAPER 2 NOTES

Trigonometry

360º = 2π radians

180º = π radians

90º = π   radians

                2

60º = π radians

                3

45º = π   radians

                 4

30º = π  radians

                 6

 

Arc length, l = rθ

Area of sector = ½r²θ

 

Tanθ = sin θ

                     Cosθ

Sin²θ + cos²θ = 1

1 + cot²θ = cosec²θ

cotθ = cosθ

                  sinθ

1 + tan²θ = sec²θ

 

sin (-θ) = -sinθ

cos(-θ) = cosθ

tan(-θ) = -tanθ

 

tan(A+B) = tanA + tanB

                                  1 – tanAtanB

tan(A-B) = tanA – tan B

                                 1 + tanAtanB

 

sin(A+B) = sinAcosB + cosAsinB

sin(A-B) = sinAcosB – cosAsinB

cos(A+B) = cosAcosB – sinAsinB

cos(A-B) = cosAcosB +sinAsinB

 

2sinAcosB = sin(A+B) + sin(A-B)

2cosAsinB = sin(A+B) – sin(A-B)

2cosAcosB = cos(A+B) + cos(A-B)

2sinAsinB = cos(A-B) – cos(A+B)

 

cos2A = cos²A – sin²A

            = 2cos²A – 1

            = 1 – 2sin²A

sin2A = 2sinAcosA

tan2A = 2tanA

                         1-tan²A

 

sin3A =3sinA – 4sin³A

 

cos²A = ½(1 + cos2A)

sin²A = ½(1 – cos2A)

 

If  2cos3Asin2A = 0

          Then cos3A=0    sin2A=0

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