Trigonometry

From ZuluNotes - Free Leaving Cert Notes

360º = 2π radians

180º = π radians

90º = radians

60º = radians

45º = radians

30º = radians

Arc length, l = rθ

Area of sector = ½r²θ

Tanθ =

Sin²θ + cos²θ = 1

1 + cot²θ = cosec²θ

cotθ =

1 + tan²θ = sec²θ

sin (-θ) = -sinθ

cos(-θ) = cosθ

tan(-θ) = -tanθ

tan(A+B) =

tan(A-B) =

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

cos2A = 2cos²A – 1

cos2A = 1 – 2sin²A

sin2A = 2sinAcosA

tan2A =

sin3A =3sinA – 4sin³A

cos²A = ½(1 + cos2A)

sin²A = ½(1 – cos2A)

If 2cos3Asin2A = 0

Then cos3A=0 sin2A=0