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Answers To The Exercises: 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14
Lesson 6
 


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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