Cambridge International Mathematics

Proof(for a triangle with acute angleA): Consider triangle ABC shown. Using Pythagoras’ theorem, we find b^2 =h^2 +x^2 ,soh^2 =b ...

C A98° B 21 cm 15 cm P R Q 4.8 km 38° 6.7 km K L M 10.3 m 72° 14.8 m AB C 9m 11 m 14 m Example 9 Self Tutor Find the size of ABC ...

4 Find: a the smallest angle of a triangle with sides 9 cm, 11 cm and 13 cm b the largest angle of a triangle with sides 3 cm, 5 ...

By the cosine rule, b^2 =a^2 +c^2 ¡ 2 accosB ) b^2 =63^2 +74^2 ¡ 2 £ 63 £ 74 £cos 58o ) b^2 ¼ 4504 : 03 ) b¼ 67 : 1 ) the aircra ...

12 Xis 20 km north of Y. A mobile telephone mast M is to be placed 15 km from Y so the bearing of M from X is 140 o. a Draw a sk ...

EXERCISE 29F 1 A 40 m high tower is 8 m wide. Two students A and B are on opposite sides of the top of the tower. They measure t ...

7 Jane and Peter are considering buying a block of land. The land agent supplies them with the given accurate sketch. Find the a ...

EXERCISE 29G.1 1aBy findingx-coordinates of points on the unit circle, copy and complete: μ 0 o 30 o 60 o 90 o 120 o 150 o 180 o ...

THE GRAPH OF y= sinx Instead of usingμ, we now usexto represent the angle variable. Thesine graphhas the following properties: ² ...

THE GRAPH OF y= tanx The vertical lines x=§ 90 o, x=§ 270 o, x=§ 450 o, and so on, are all vertical asymptotes. The tangent curv ...

7 a y= sinx b y= sinx+2 c y= sin(x+90o) d y= cosx What do you notice? 8 a y= cosx b y= cosx¡ 2 c y= cos(x¡ 90 o) d y= sinx What ...

Example 12 Self Tutor Draw free-hand sketches of y= sinx, y= 3 sinx and y= 3 sin(2x) for 0 o 6 x 6720 o. EXERCISE 29H 1 Draw fre ...

ef 5 Findaandbif y=acos(bx) has graph: ab cd ef Review set 29A 1 Find: a the exact coordinates of point P b the coordinates of P ...

4 The area of triangle ABC is 21 m^2. Findx. 5 Use the diagram alongside to write, in terms ofaandb, a value for: a cosμ b sinμ ...

2 Triangle ABC has acute angleμoat vertex A. Findμ correct to 1 decimal place if the area of triangle ABC is 33 : 4 cm^2. 3aStat ...

Challenge #endboxedheading 10 The illustrated graph has equation of the form y=asin(bx). Findaandb. 11 2 1 O 180° 360° y x Use y ...

Variation and power modelling 30 Contents: A Direct variation [2.13] B Inverse variation [2.13] C Variation modelling [2.13] D P ...

Two variables aredirectly proportionalif multiplying one of them by a number results in the other one being multiplied by the sa ...

EXERCISE 30A.1 1 h^012345 W 0 12 : 50 25 : 00 37 : 50 50 : 00 62 : 50 The table alongside shows the total wages $Wearned for wor ...

OTHER DIRECT VARIATION The formula for finding the areaAof a circle of radiusr,is A=¼r^2. r 0 1 2 3 4 A 0 3 : 14 12 : 57 28 : 27 ...