06.02b Applying the Laws of Sines and Cosines

• Respond to the following prompt in a word processing document. Describe, in detail, when to use the law of cosines, the law of sines, and the law of sines with the ambiguous case. Provide general guidelines, in your own words, for each law that can be applied to any triangle situation with which you are presented. To aid in your explanation, you may refer to specific problems from the text.
• Your response must include:
  • A discussion of
    • The law of cosines
    • The law of sines
    • The ambiguous case (law of sines)
  • General guidelines in your own words that can be applied to any triangle.
  • Words in complete sentences with appropriate grammar and spelling.
  • Provide the source used for information (i.e. the website, the book, etc.). Not providing your source may result in an Academic Integrity violation.

Use mathematical induction to prove the statement is true for all positive integers n, or show why it is false. (4 points each.)

1. 46 + 57 + 68 + ... + 4n( 4n + 2) =
2. 1²+ 4²+ 7²+ ... + (3n - 2)²=

For the given statement P_n, write the statements P₁, P_k, and P_k+1. (2 points)

1. 2 + 4 + 6 + . . . + 2n = n(n+1)