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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.