Determine the quarter points.
y=cos(x−5π/2)
(Type an exact answer, using π as needed. Use integers or fractions for any numbers in the expression.)
- Please show step by step work. Show how you're getting the numbers/answers because I want to learn it. Thank You.
y=cos(x−5π/2)
amplitude = 1
period = 2π
If we had the simple curve y = cos x
the quarter points would be
(0,1) , (π/2, 0) , (π, -1), (3π/2 , 0) , and repeating at (2π, 1)
but we shifted our basic cosine curve 5π/2 units to the right, so our points are:
(0 + 5π/2, 1), (π/2 + 5π/2, 0) , (π + 5π/2, -1) .....
or
(5π/2, 1) , (3π , 0) , (7π/2, -1) , ....
remember that the period is 2π
so we can add or subtract 2π to get more or other points
(5π/2 - 2π,1) , (3π - 2π, 0) , (7π/2, -1) , ....
(π/2, 1) , (π,0), (3π/2 , -1), ...
ahhhh , but that is the same as y = sin(x)
check:
http://www.wolframalpha.com/input/?i=y%3Dcos(x%E2%88%925%CF%80%2F2)
THANK YOU SOOO MUCH REINY!! GOD BLESS YOU. YOU'RE AMAZING!
ahhhh , but that is the same as y = sin(x)
:)
To determine the quarter points of the equation y = cos(x - 5π/2), we need to find the values of x where the cosine function equals 1/4 and 3/4.
Step 1: Identify the period of the cosine function.
The period of the cosine function is 2π since cos(x) completes one full cycle every 2π units. In this case, the x inside the cosine function is (x - 5π/2), which means the cycle is shifted to the right by 5π/2 units.
Step 2: Find the shift and adjust the limits accordingly.
To find the shift, set x - 5π/2 equal to zero and solve for x:
x - 5π/2 = 0
x = 5π/2
This means the cosine function is shifted 5π/2 units to the right. To find the quarter points, we need to find the x-values where the cosine function equals 1/4 and 3/4, within the shifted cycle.
Step 3: Find the x-values for the quarter points.
Since we know the period is 2π and the cycle is shifted 5π/2 units to the right, we can start from the shift and add intervals of π/2 to find the quarter points.
For the first quarter point (cos(x) = 1/4):
x = 5π/2 + π/2 = 6π/2 + π/2 = 7π/2
For the third quarter point (cos(x) = 3/4):
x = 5π/2 + 3π/2 = 8π/2 + 3π/2 = 11π/2
Therefore, the quarter points of y = cos(x - 5π/2) are x = 7π/2 and x = 11π/2.
Note: The values are given in terms of π because it allows for exact representation of the angles and preserves the trigonometric values.