6.1.
The distance is equal to |7 – (–9)|
= |7 + 9| = 16.
6.2.
6.3.
= 60°. In 1) – 3), 
= 30°. In 4),
= 0°
6.4.
We can use the "queen" formula (6.2): 
6.5.
6.6.
6.7.
1) Consider the queen formula cos(
- )
= cos·cos
+ sin·sin
and
set
= 0. Then cos
= 1 and sin
= 0.
The queen formula becomes:
cos (-)
= cos.
2) In queen formula, set
= 90°. Use the values: cos 90° = 0, sin 90° =
1.
6.8.
1) If
= ,
the queen formula becomes: cos 0 = 1 = cos2
+ sin2.
This is the main identity: sin2
+ cos2
= 1.
2) If
= – ,
the queen formula becomes:
cos 2
= cos·cos(–)
+ sin·sin(–),
or, cos 2
= cos2–
sin2.
This is the "cosine of the double angle"
formula.
3) If
= –  ,
the queen formula becomes: cos [–(–
)]
= cos·cos(–
)
+ sin·sin(–
),
or cos (
+ )
= cos·cos
–
sin·sin
.
This is the "cosine of the sum" formula.
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