Hi i posted this before but I wanted to ask Bobpursley a few questions on his reply
1)For the first function you used cosine when they ask for sin, why is that? Also why did you put .5 in the beginning and end of the function?
2)For the second question why did you put 10 in front of the cos instead of 20?
The sun always illuminates half of the moon’s surface, except during a lunar eclipse. The illuminated portion of the moon visible from Earth varies as it revolves around Earth resulting in the phases of the moon. The period from a full moon to a new moon and back to a full moon is called a synodic month and is 29 days, 12 hours, and 44.05 minutes long. Write a sine function that models the fraction of the moon’s surface which is seen to be illuminated during a synodic month as a function of the number of days, d, after a full moon. [Note: full moon equals illuminated.]
I am really confused on this one I know I have to make a sine function.
so would it be like y= 29sin(pi/6*t)+44.05
sorry that was probably a really bad guess.
2)A bicycle tire has a diameter of 20 inches and is revolving at a rate of 10 rpm. At t = 0, a certain point is at height 0. What is the height of the point above the ground after 20 seconds?
Guessing because I have not seen original:
cos instead of sin because it begins with full moon, cos 0 = 1 but sin 0 = 0
The half of the moon opposite the sun remains dark. Only 1/2 the moon can be illuminated.
The diameter of the tire is 20, but the radius is 10 which is the dimension you want to use.
1) In the first question, it seems that you are referring to a previous response by Bobpursley. Unfortunately, without the actual response, I cannot provide a specific explanation. However, I can help clarify some general concepts.
When dealing with trigonometric functions, it is important to understand the relationship between different trigonometric ratios. The sine function (sin) and cosine function (cos) are related by a phase shift of pi/2 radians (or 90 degrees). This means that if you have a sine function, you can obtain its corresponding cosine function by shifting it to the left by pi/2 radians (or 90 degrees).
Regarding the use of the value 0.5 at the beginning and end of a function, without further context it is difficult to provide a definite explanation. However, sometimes a function may be scaled or shifted to fit a particular range or to match certain criteria. The value 0.5 could be used to scale the function between 0 and 1, or it could represent a specific condition or requirement mentioned in the problem statement.
2) Similarly, without the specific response from Bobpursley, it is challenging to provide a precise explanation. However, if a cosine function is used to model a height or distance, the coefficient in front of the cosine function determines the amplitude or maximum value of the function. This coefficient can affect how the function oscillates or varies over time.
In the case you mentioned, if the coefficient in front of the cosine function is 10 instead of 20, it could indicate a different scaling or amplitude requirement in this particular problem. The value of 10 may be chosen to fit the given scenario or to satisfy specific constraints.
Overall, it's essential to consider the specific context of the problem and any additional information or instructions provided to better understand the reasoning behind the choices made in the responses.