Question

We often reason with trigonometric identities such as sin^2(x) + cos^2(x) = 1. Given a set of such identities S and an identity to prove using the set S, what would be the most efficient data structure and algorithm for this purpose. Justify your answer. Explain the representation of the identities with an example.

Answer #1

Given sin(theta) = 1/2 and cos(theta) = (sqrt(3))/2 Find the
exact values of the four remaining Trigonometric functions of theta
using identities.

- Given cos(x)=-1/12 with 180°<x<270°. Find cos(x/2)
- Given sin(x)= (squareroot 5)/3 where x is an acute angle. Find
sin(x/2)

(1) Recall on February 6 in class we discussed e 0 + e 2πi/n + e
4πi/n + · · · + e 2(n−1)πi/n = 0 and in order to explain why it was
true we needed to show that the sum of the real parts equals 0 and
the sum of the imaginary parts is equal to 0.
(a) In class I showed the following identity for n even using
the fact that sin(2π − x) = − sin(x):...

A standing wave on a string fixed at both ends is described by
y(x,t)=2 sin((π/3)x)cos((π/3)t), where x and y are given in cm and
time t is given in s. Answer the following questions
a) Find the two simplest travelling waves which form the above
standing wave
b) Find the amplitude, wave number, frequency, period and speed of
each wave(Include unit in the answer)
c) When the length of the string is 12 cm, calculate the distance
between the nodes...

(a) Suppose you are given the following (x, y)
data pairs.
x
1
2
5
y
2
1
7
Find the least-squares equation for these data (rounded to three
digits after the decimal).
ŷ = + x
(b) Now suppose you are given these (x, y) data
pairs.
x
2
1
7
y
1
2
5
Find the least-squares equation for these data (rounded to three
digits after the decimal).
ŷ = + x
(c) In the data for parts (a) and (b), did...

Suppose you are given the following (x, y)
data pairs.
x
1
2
6
y
4
3
9
Find the least-squares equation for these data (rounded to three
digits after the decimal).
ŷ = + x
(b) Now suppose you are given these (x, y) data
pairs.
x
4
3
9
y
1
2
6
Find the least-squares equation for these data (rounded to three
digits after the decimal).
ŷ = + x
(c) In the data for parts (a) and (b), did we...

a) Suppose you are given the following (x, y)
data pairs.
x
2
3
6
y
4
3
7
Find the least-squares equation for these data (rounded to three
digits after the decimal).
ŷ = + x
(b) Now suppose you are given these (x, y) data
pairs.
x
4
3
7
y
2
3
6
Find the least-squares equation for these data (rounded to three
digits after the decimal).
ŷ = + x
(c) In the data for parts (a) and (b), did...

CASE: Advertising Experiments at RestaurantGrades Shirley A.
Critic is the founder of RestaurantGrades (RG), a restaurant review
platform (similar to Yelp or TripAdvisor) with an impressive stock
of online reviews written by ordinary restaurant-goers.Shirley is
happy with the company’s growth and position in the industry, and
has compelling evidence that RG reviews have an important influence
on the restaurant choices people make. However, doubts have been
raised about the efficacy of the company’s main source of
revenue—selling ads to restaurants....

Item 1
In the case below, the original source material is given along
with a sample of student work. Determine the type of plagiarism by
clicking the appropriate radio button.
Original Source Material
Student Version
I accept the point that whenever learning occurs, some medium or
mix of media must be present to deliver instruction. However,
if learning occurs as a result of exposure to any media,
the learning is caused by the instructional method embedded in the
media presentation....

Item 6
In the case below, the original source material is given along
with a sample of student work. Determine the type of plagiarism by
clicking the appropriate radio button.
Original Source Material
Student Version
The theory we have constructed originates with the three phases
of learning described above. We have organize and adapted the
features of simulations to provide the learner with the
most effective and efficient presentations in order to achieve
successful acquisition, application and assessment.
Our general...

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