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[Index]

   Introduction Introduction
   What's the essence? Essence
   Memorizing Memorizing
   Understanding Understanding
   Summarizing Summarizing
   Examples Examples

Example 1
Example 2
Example 3
Example 4
Example 5
Example 6
Example 7
Example 8
General ideas

   Exercises Exercises
   Final thoughts Final thoughts
     
ready for the last one?
Page 1 | Page 2 | Page 3 | Page 4 | Page 5 | Proof(s)

Example 8--Page 2

We see that we already got the major part of the goal identity:

6_8201.gif (2211 bytes)

Using our compare strategy, we claim that

6_8202.gif (2926 bytes) (6)         

Let's compare what are the differences between equation (6) and equations (1) and (2). We see (1) and (2) have c, but (6) doesn't have a c. How can we get an equation from (1) and (2) which has no c. This clue tells us to make subtraction between (1) and (2) we have:

6_8203.gif (2974 bytes) (7)         

To get the angle tht_p_phi_2.gif (1119 bytes), we use the Sum to Product formulas, and get:

6_8204.gif (3591 bytes)

6_8205.gif (3053 bytes) (8)         

In the given conditions, there is one condition about both theta.gif (908 bytes) and phi.gif (942 bytes). To see the relationship between theta.gif (908 bytes) and phi.gif (942 bytes), we change around tht_n_p_2kpi.gif (1673 bytes), as follows:

6_8206.gif (2902 bytes)

Where k is an integer. So, the condition says:

6_8207.gif (2116 bytes)

Because 6_8208.gif (1550 bytes), from equation (8), we have:

6_8209.gif (2399 bytes) (9)         
     
  

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LWR
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Copyright 1998 LWR, ThinkQuest team 17119. All rights reserved.