Cambridge International Mathematics

a angle AOP= (180o¡μ)

biPis(cos(180o¡μ),sin(180o¡μ))

ii Pis(¡cosμ,sinμ)

c cos(180o¡μ)=¡cosμ and sin(180o¡μ) = sinμ

d tan(180o¡μ)=

sin(180o¡μ)

cos(180o¡μ)

=

sinμ

¡cosμ

fusingcg

=¡tanμ

EXERCISE 29A.1

1a

b Find the coordinates of P correct to 3 decimal places.

2 Use the unit circle diagram to find:

a sin 180o b cos 180o c sin 270o d cos 270o

e cos 360o f sin 360o g cos 450o h sin 450o

3 Use the unit circle diagram to estimate, to 2 decimal places:

a cos 50o b sin 50o c cos 110o d sin 110o

e sin 170o f cos 170o g sin 230o h cos 230o

i cos 320o j sin 320o k cos(¡ 30 o) l sin(¡ 30 o)

4 Check your answers to 3 using your calculator.

tanμ=

sinμ

cosμ

5aState the coordinates of point P.

b Find the coordinates of Q using:

i the unit circle

ii symmetry in thex-axis.

c What can be deduced fromb?

d Usecto simplifytan(¡μ):

6 By considering a unit circle diagram like that in 5 , show how to simplify

sin(180o+μ), cos(180o+μ), and tan(180o+μ).

Hint: Consider rotational symmetry.

x

y

O 1

1

-1

-1

231°

P

x

y

O 1

A

1

-1

-1

q

P

-q Q

State the exact coordinates of P.

Further trigonometry (Chapter 29) 581

IGCSE01

cyan magenta yellow black

(^05255075950525507595)
100 100
(^05255075950525507595)
100 100
Y:\HAESE\IGCSE01\IG01_29\581IGCSE01_29.CDR Monday, 27 October 2008 2:52:32 PM PETER