Further trigonometry

29

Opening problem

A triangular property is bounded by two roads and

a long, straight drain.

Can you find:

a the area of the property in m^2 and in hectares

b the length of the drain boundary

c the angle that the Johns Road boundary makes

with the drain boundary?

InChapter 15we introduced theunit circle, which is the

circle with centre O(0,0)and radius 1 unit. In that chapter

we considered only the first quadrant of the circle, which

corresponds to anglesμwhere 0 o 6 μ 690 o. We now consider

the complete unit circle including all four quadrants.

As P moves around the circle, the angleμvaries.

The coordinates of P are defined as(cosμ,sinμ).

A THE UNIT CIRCLE [8.3]

120°

Johns Road

Evans Road

277 m 324 m

drain

x

y

O

q

1

A

1

-1

-1

P cos ,( ¡q ¡sin¡q)

Contents:

A The unit circle [8.3]

B Area of a triangle using sine [8.6]

C The sine rule [8.4]

D The cosine rule [8.5]

E Problem solving with the

sine and cosine rules [8.4, 8.5, 8.7]

F Trigonometry with compound

shapes [8.1, 8.4, 8.5, 8.7]

G Trigonometric graphs [3.2, 8.8]

H Graphs of y=asin(bx) and

y=acos(bx) [3.2, 3.3, 8.8]

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Y:\HAESE\IGCSE01\IG01_29\579IGCSE01_29.CDR Tuesday, 18 November 2008 11:07:41 AM PETER