Cambridge Additional Mathematics

GRAPHING

PACKAGE

30 °

210 °

O

&],Qw*

&-],-Qw*

246 Trigonometric functions (Chapter 9)

6 Solve tanx=

p

3 for 06 x 62 ¼. Hence solve the following equations for 06 x 62 ¼:

a tan 4x=

p

3 b tan^2 x=3

7 Solve

p

3 tan 3x=1for 06 x 6 ¼.

8 Solve for ¡¼ 6 x 6 ¼:

a secx=¡ 2 bccotx=0

Example 10 Self Tutor

Find the exact solutions of

p

3 sinx= cosx for 0 ± 6 x 6360 ±.

p

3 sinx= cosx

)

sinx

cosx

=p^13 fdividing both sides by

p

3 cosxg

) tanx=p^13

) x=30± or 210 ±

9 Solve for 06 x 62 ¼:

a sinx¡cosx=0 b sinx=¡cosx

c sin 3x= cos 3x d sin 2x=

p

3 cos 2x

Check your answers using the graphing package.

10 Solve for 06 x 6 ¼: sinx= cosecx

There are a vast number of trigonometric relationships. However, we only need to remember a few because

we can obtain the rest by rearrangement or substitution.

SIMPLIFYING TRIGONOMETRIC EXPRESSIONS

For any given angleμ, sinμ and cosμ are real numbers. tanμ is also real whenever it is defined. The

algebra of trigonometry is therefore identical to the algebra of real numbers.

An expression like 2 sinμ+ 3 sinμ compares with 2 x+3x,so2 sinμ+ 3 sinμ= 5 sinμ.

To simplify more complicated trigonometric expressions, we often use the identities:

sin^2 μ+ cos^2 μ=1

tanμ=

sinμ

cosμ

tan^2 μ+ 1 = sec^2 μ

1 + cot^2 μ= cosec^2 μ

F Trigonometric relationships

sin 2 μμ+=1cos is a special

form of Pythagoras theorem

2

’

p

3 cosec2x=2

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Additional Mathematics
Y:\HAESE\CAM4037\CamAdd_09\246CamAdd_09.cdr Wednesday, 15 January 2014 10:42:14 AM BRIAN