1) The document discusses compound angle formulas and how to use them to solve exam-type questions. It provides examples of using the formulas sin(A+B) and cos(A-B) to find exact values of trigonometric functions of compound angles. 2) Key questions are provided to practice applying the compound angle formulas to find the exact values of sin DAC, cos DAC, and sin HFT using information given in diagrams.

1. Block 2
Compound Angle Formulae

2. What is to be learned?
• How to deal with exam type questions
involving compound angles formulas.

3. A
C
B
D
Write the exact value of sin DAB
3
5
LDAB = 90 + x
x
sin DAB = sin (90 + x)
Mark Angle
Write like a formula Cos(A – B ) etc.
Exam Type Question

4. A
C
B
D
3
5
x
sin (90 + x) = sin 90 cos x + cos90 sin x
? ?
sin x = 3
/5
cos x
√ (52
– 32
)
4
= 4
/5
= 1(4
/5) + 0(3
/5)
= 4
/5
Calculate Missing Values
using sin(A + B)
formula

5. 1. Calculate the exact value of Cos DFG
Cos DFG = Cos(x + y)
Cos (x + y) = Cosx Cosy – Sinx Siny
= 1
/√5 X 1
/√10 – 2
/√5 X 3
/√10
= 1
/√50 – 6
/√50
= -5
/√50
= - 1
/
F
D G
E
√10
32
X Y
1
Using Pythag
√5
Key Question

6. x
x
4
3
2. Find the exact value of
a) Sin DAC
b) Cos DAC
3. Find the exact value of
Sin HFT.
A
B
C
D
3√7
/8
1
/8
F
G
H
T
x
5
√21
2
/5

7. x
x
4
3
2. Find the exact value of
a) Sin DAC
b) Cos DAC
3. Find the exact value of
Sin HFT.
A
B
C
D
3√7
/8
1
/8
F
G
H
T
x
5
√21
2
/5