Cambridge International AS and A Level Mathematics Pure Mathematics 1

Trigonometry P1^ 7 ●?^ How can you find further roots of the equation 3tan θ^ =^ −1, outside the range −180°  θ  180°? ExAmPlE ...

P1^ 7 Exercise (^) 7C ExAmPlE 7.8 Solve the equation 2sin^2 θ = cos θ + 1 for 0°  θ  360°. SOlUTION First use the identity sin ...

Trigonometry 234 P1^ 7 2  (i) Sketch the curve y = cos x for −90°  x  450°. (ii) Solve the equation cos x = 0.6 for −90°  x  ...

P1^ 7 Circular measure 235 9  The diagram shows part of the curves y = cos x° and y = tan x° which intersect at the points A and ...

Trigonometry P1^ 7 The grade (mode ‘gra’) is a unit which was introduced to give a means of angle measurement which was compatib ...

P1^ 7 Circular (^) measure ExAmPlE 7.9 (i) Express in radians (a) 30° (b) 315° (c) 29°. (ii) Express in degrees (a) π 12 (b) 8 3 ...

Trigonometry 238 P1^ 7 ExAmPlE 7.11 Solve tan^2 θ = 2 for 0  θ  π. SOlUTION Here the range 0  θ  π indicates that radians ar ...

P1^ 7 The area of a sector of a circle 5  Solve the following equations for −π  θ  π. (i) sin θ = 0.2 (ii) cos θ = 0.74 (iii) ...

Trigonometry P1^ 7 The following formulae often come in useful when solving problems involving sectors of circles. For any trian ...

P1^ 7 Exercise (^) 7E (ii) Use the cosine rule to find the length of the chord AB a^2 = b^2 + c^2 − 2 bc cos A Substitute in b = ...

Trigonometry 242 P1^ 7 (ii) The diagram shows two circles, each of radius 4 cm, with each one passing through the centre of the ...

P1^ 7 Exercise (^) 7E 243 7  In the diagram, OAB and OCD are radii of a circle, centre O and radius 16 cm. Angle AOC = α radians ...

Trigonometry P1^ 7 10  In the diagram, AB is an arc of a circle, centre O and radius r cm, and angle AOB = θ radians. The point ...

P1^ 7 Other trigonometrical functions ACTIvITy 7.3  Figure 7.33 shows the graphs of y = sin x and y = 2 + sin x for 0°  x  360 ...

Trigonometry 246 P1^ 7 Reflections ACTIvITy 7.5  Figure 7.35 shows the graphs of y = sin x and y = –sin x for 0°  x  360°. Des ...

Other (^) trigonometrical (^) functions 247 P1^ 7 ACTIvITy 7.7 Figure 7.37 shows the graphs of y = sin x and y = sin 2x for 0°  ...

Trigonometry P1^ 7 (ii) The curve of y = 3 + cos x is obtained from that of y = cos^ x by a translation 0 3    . The curve ...

Other (^) trigonometrical (^) functions P1^ 7 (iv) The curve of y = 2 cos x is obtained from that of y = cos x by a stretch of s ...

Trigonometry 250 P1^ 7 (b) f : x  4 + 2 sin x The maximum value of sin x is 1. So the maximum value of f is 4 + 2 × 1 = 6. The ...

Exercise (^) 7F P1^ 7 ExERCISE 7F  1  Starting with the graph of y = sin x, state the transformations which can be used to sketc ...