Five questions: Law of sines, law of cosines, vectors in the plane, vectors and dot products, trigonometric form of complex numbers.
Unformatted Attachment Preview
Question 1: Law of Sines
Can the Law of Sines be used to solve a right triangle? Write a short paragraph explaining why it
can or cannot be used. If it can be used, explain how to use it. Is there an easier way to solve the
Question 2: Law of Cosines
Describe how the Law of Cosines can be used to solve the ambiguous case of the oblique
triangle ABC, where a = 12 feet, b = 30 feet, and A = 20°. Is the result the same as when the Law
of Sines is used to solve the triangle? Describe the advantages and the disadvantages of each
Question 3: Vectors in the Plane
1. In your own words, state the difference between a scalar and a vector. Give examples of each.
2. Give geometric descriptions of the operations of addition of vectors and multiplication of a
vector by a scalar.
Question 4: Vectors and Dot Products
What is known about T, the angle between two nonzero vectors u and v, if each of the following
is true? Explain your answers.
1. u v = 0
2. u v > 0
3. u v < 0 Question 5: Trigonometric Form of Complex Numbers The famous formula shown below is called Eulers formula, after the Swiss mathematician Leonhard Euler (1707-1783). ea + bi = ea(cos b + i sin b)
This formula gives rise to the equation epi + 1 = 0. This equation related the five most famous
numbers in mathematics–0, 1,p , e, and i– in a single equation. Show how Eulers formula can
be used to derive this equation. Write a short paragraph summarizing your work.
Purchase answer to see full
Delivering a high-quality product at a reasonable price is not enough anymore.
That’s why we have developed 5 beneficial guarantees that will make your experience with our service enjoyable, easy, and safe.
You have to be 100% sure of the quality of your product to give a money-back guarantee. This describes us perfectly. Make sure that this guarantee is totally transparent.Read more
Each paper is composed from scratch, according to your instructions. It is then checked by our plagiarism-detection software. There is no gap where plagiarism could squeeze in.Read more
Thanks to our free revisions, there is no way for you to be unsatisfied. We will work on your paper until you are completely happy with the result.Read more
Your email is safe, as we store it according to international data protection rules. Your bank details are secure, as we use only reliable payment systems.Read more
By sending us your money, you buy the service we provide. Check out our terms and conditions if you prefer business talks to be laid out in official language.Read more