Cambridge International AS and A Level Mathematics Pure Mathematics 1

Integration P1^ 6 EXERCISE 6H  1  Name six common objects which are solids of revolution. 2  In each part of this question a reg ...

Exercise (^) 6H P1^ 6 6  The graph shows the curve y = x^2 − 4. The region R is formed by the line y = 12, the x axis, the y axi ...

Integration P1^ 6 8  The diagram shows part of the curve y a x = , where a is a positive constant. Given that the volume obt ...

Key (^) points P1^ 6 4  Area B =∫a((fgxx)– ())dx b 5  Area C =∫pxy q d 6 Volumes of revolution About the x axis V = (^) ∫ b a ...

Trigonometry 216 P1^ 7 Trigonometry I must go down to the seas again, to the lonely sea and the sky,   And all I ask is a tall s ...

P1^ 7 Trigonometrical functions Trigonometrical functions The simplest definitions of the trigonometrical functions are given in ...

Trigonometry 218 P1^ 7 From triangle ABD, sin; 60 23 cos; 60 1 tan; 2 °= °= 60 °= 3 sin; 60 °= 23 cos; 60 °= 21 tan; 60 °= 3 sin ...

P1^ 7 Trigonometrical (^) functions 219 If you imagine the angle at X becoming smaller and smaller until it is zero, you can ded ...

Trigonometry P1^ 7 Positive and negative angles Unless given in the form of bearings, angles are measured from the x axis (see f ...

P1^ 7 Exercise (^) 7A 221 In triangle BCD, tan θ = = BD BC 3 3 1 3 l l ⇒ θ = tan–1 1 3     = 30° ExERCISE 7A  1  In t ...

Trigonometry 222 P1^ 7 5  In the diagram, ABED is a trapezium with right angles at E and D, and CED is a straight line. The leng ...

P1^ 7 Trigonometrical (^) functions (^) for (^) angles (^) of (^) any (^) size First look at the right-angled triangle in figure ...

Trigonometry P1^ 7 an equation: it is true when θ = 45° or 225°, but not when it takes any other value in the range 0°  θ  360 ...

P1^ 7 Exercise (^) 7B 225 Method 2 When one side of the identity looks more complicated than the other side, you can work with t ...

Trigonometry P1^ 7 10  Prove the identity^1 1 + + 2 + sin ≡ cos cos sincos x x x xx [Cambridge AS & A Level Mathematics 9709 ...

P1^ 7 The sine and cosine graphs Figure 7.14 shows the circle in this new orientation, together with the resulting graph. For an ...

Trigonometry P1^ 7 The tangent graph The value of tan θ can be worked out from the definition tan θ = y x or by using tan θ = si ...

P1^ 7 Solving equations using graphs of trigonometrical functions Solving equations using graphs of trigonometrical functions Su ...

Trigonometry P1^ 7 –0.5 –1 –360° –270° –180° –90° 0 90° 180° 270° 360°θ 1 0.5 y y = cos θ principal values –0.5 –1 –360° –270° – ...

P1^ 7 Solving (^) equations (^) using (^) graphs (^) of (^) trigonometrical (^) functions 231 ExAmPlE 7.5 Find values of θ in th ...