Specialist Maths Trigonometry Review Week 3. Addition Formulae

Specialist Maths

Trigonometry Review

Week 3

Addition Formulae

BABABA sincoscossinsin

BABABA sincoscossinsin

BABABA sinsincoscoscos

BABABA sinsincoscoscos

Duplication Formulae

AAA cossin22sin

A

A

AAA

2

2

22

sin21

1cos2

sincos2cos

Sum or Difference to a Product

2sin

2sin2coscos

2cos

2cos2coscos

2cos

2sin2)sinsin

BABABA

BABABA

BABABA

Product to Sum or a Difference

)cos()cos(sinsin2

)cos()cos(coscos2

)sin()sin(cossin2

BABABA

BABABA

BABABA

Example 14 (Ex1D)

xBxA

x

cossin form in the

answeryour writeand 3

2sin Expand

Solution 14

xBxA

x

cossin form in the

answeryour writeand 3

2sin Expand

Example 15 (Ex 1D)

BABA

αααα

coscossinsin (b)

sin4coscos4sin(a)

:Simplify

Solution 15

BABA

αααα

coscossinsin (b)

sin4coscos4sin(a)

:Simplify

Example 16 (Ex 1D)

.calculator a using without 2sin

of value thefind ,2

where13

5sin If

α

Solution 16

.calculator a using without 2sin

of value thefind ,2

where13

5sin If

α

Example 17 (Ex 1D)

tancotsincos

cos that Prove

Solution 17

tancotsincos

cos that Prove

Example 18 (Ex 1D)

tansin2

cos2-1 that Prove

Solution 18

tansin2

cos2-1 that Prove

Example 19 (Ex 1D)

2cot2cosec2sec2

1cosec

2

1 that Show 22

Solution 19

Solving Trigonometric Equations (Ex 1E1)

3 6 9 12 15 18 21 24

60sin (2) 40sin (1)

24x0for solve

and singraph toCalculatoryour Use

.-x.x

xy

Example 20 (Ex 1E2)30for ,

2

1sinlly algebraica Solve xx

Solution 2030for ,

2

1sinlly algebraica Solve xx

Example 21 (Ex 1E2) xx for ,032coslly algebraica Solve

Solution 21 xx for ,032coslly algebraica Solve

Example 22 (Ex 1E2)

30for ,

2

1

3sinlly algebraica Solve

xx

Solution 22

30for ,

2

1

3sinlly algebraica Solve

xx

Example 23 (Ex 1E2)20for ,

2

32coslly algebraica Solve xx

Solution 2320for ,

2

32coslly algebraica Solve xx

Example 24 (Ex 1E2)

places. decimal 2 toaccurateanswer your Give

.20for ,4

3sinlly algebraica Solve xx

Solution 24

places. decimal 2 toaccurateanswer your Give

.20for ,4

3sinlly algebraica Solve xx

Example 25 (Ex 1E2)20for ,1coscos2lly algebraica Solve 2 xxx

Solution 2520for ,1coscos2lly algebraica Solve 2 xxx

This Week

• Text book P29 – 37

Ex1D Q1-16;

1E1 Q1;

1E2 Q1-4.

• Review Sets 1A,1B.