Your Practice Paper – Analysis and Approaches HL for IBDP Mathematics
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2-D Trigonometry
� Consider a triangle ABC : sin A sin B a b
1 . � or � : Sine rule a b sin A sin B Note : The ambiguous case exists if two sides and an angle are known , and the angle is opposite to the shorter known side
2 .
3 . b �c �a � � � or cos A �
2bc
1 absin
C : Area of the triangle ABC
2
2 2 2 a b c 2bc cos A
2 2 2
: Cosine rule
x yrad
� � : Method of conversions between degree and radian 180 � rad
� Consider a sector OPRQ with centre O , radius r and �POQ � � in radian : 1 . r� : Arc length PQ
2 .
3 .
1 2 r � : Area of the sector OPRQ 2
1 2
( sin ) 2 r � � � : Area of the segment PRQ
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Areas and Volumes
� For a cube of side length l : 1 . 2 .
2
6l : Total surface area
3 l : Volume
� For a cuboid of side lengths a , b and c :
1 . 2 ( ab �bc � ac)
: Total surface area
2 . abc : Volume
� For a prism of height h and cross-sectional area A : 1 . Ah : Volume
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