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Core Mathematics 3

Formulae
Exponentials and Logarithms ln = ln

Trigonometry sin - = - sin
cos - = cos
tan - = - tan

sin = cos ( - )
2

cos = sin ( 2 - )
sin
tan = cos
1
cosec = sin
1
sec =…

Page 2

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+ -
sin + sin = 2 sin cos
2 2
+ -
sin - sin = 2 cos sin
2 2
+ -
cos + cos = 2 cos 2 cos 2
+ -
cos - cos = -2 sin 2 sin 2
1
sin cos = 2 [sin(…

Page 3

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Notes Tips
Numerical Know that a solution is within a range by a change of sign
Methods Know that a stationary point is within a range by a change of
sign of the gradient
Remember to justify the number of decimal places
Algebra and () = ()() + () To…

Page 4

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Trigonometry
1
sin 30° = 2 cos 30° =
3 1
tan 30° = 3 Know the graph of arcsin :
2
1 1 -intercept: (0,0)
sin 45° = cos 45° = tan 45° = 1
2 2 -intercept: (0,0)
3 1
sin 60° = cos 60° = 2 tan…

Page 5

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sin - = - sin
cos - = cos
tan - = - tan

sin = cos ( - )
4

cos = sin ( 4 - )
sin
tan = cos
1
cosec =
sin
1
sec = cos
cos 1
cot = =
sin tan
sin + cos…

Page 6

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+ -
sin + sin = 2 sin cos
2 2
+ -
sin - sin = 2 cos sin
2 2
+ -
cos + cos = 2 cos 2 cos 2
+ -
cos - cos = -2 sin 2 sin 2
sin( + ) = sin cos…

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