For the following expression, find the value of y that corresponds to each value of x, then write your results as ordered pairs (x,y).
y=7cos(x-pi/6) for x=pi/6, pi/3, 2pi/3, pi, 7pi/6
I will do the first one, you do the others.
Let me know what you get.
y = 7cos(x-π/6) , for x = π/6
= 7cos(π/6 - π/6)
= 7cos 0
= 7(1) = 7
one more... if x = 2π/3
y = 7cos(2π/3 - π/6)
= 7cos (π/2)
= 7(0) = 0
i didn't realize it was just plugging in! thanks! i just need to figure out how to subtract fractions with pi in them now
pi/3 is 7 square root 3/ 2 pi is - 7 square root 3 / 2 and 7pi/6 is -7
To find the value of y that corresponds to each value of x in the expression y = 7cos(x - π/6), we will substitute the given values of x into the expression and evaluate it.
1. For x = π/6:
y = 7cos(π/6 - π/6)
Simplifying the expression inside the cosine:
y = 7cos(0)
Since the cosine of 0 is equal to 1, the value of y is:
y = 7 * 1 = 7
Therefore, the ordered pair (x, y) for x = π/6 is (π/6, 7).
2. For x = π/3:
y = 7cos(π/3 - π/6)
Simplifying the expression inside the cosine:
y = 7cos(π/6)
The cosine of π/6 is equal to (√3)/2, so the value of y is:
y = 7 * (√3) / 2 = (7√3) / 2
Therefore, the ordered pair (x, y) for x = π/3 is (π/3, (7√3)/2).
3. For x = 2π/3:
y = 7cos(2π/3 - π/6)
Simplifying the expression inside the cosine:
y = 7cos(π/2)
The cosine of π/2 is equal to 0, so the value of y is:
y = 7 * 0 = 0
Therefore, the ordered pair (x, y) for x = 2π/3 is (2π/3, 0).
4. For x = π:
y = 7cos(π - π/6)
Simplifying the expression inside the cosine:
y = 7cos(5π/6)
The cosine of 5π/6 is equal to -√3/2, so the value of y is:
y = 7 * (-√3) / 2 = (-7√3) / 2
Therefore, the ordered pair (x, y) for x = π is (π, (-7√3)/2).
5. For x = 7π/6:
y = 7cos(7π/6 - π/6)
Simplifying the expression inside the cosine:
y = 7cos(π)
The cosine of π is equal to -1, so the value of y is:
y = 7 * (-1) = -7
Therefore, the ordered pair (x, y) for x = 7π/6 is (7π/6, -7).
In summary, the ordered pairs (x, y) corresponding to each value of x in the given expression are:
(π/6, 7)
(π/3, (7√3)/2)
(2π/3, 0)
(π, (-7√3)/2)
(7π/6, -7)
I don't like the way you wrote those answers
Be mathematically correct, ..... e.g.
if x = π/3
y = 7cos(π/3 - π/6)
= 7 cos (π/6)
= 7(√3/2) = 7√3/2
if x = 7π/6
y = 7cos(7π/6 - π/6)
= 7cos π
= 7(-1) = -7
A statement such as "π/3 is 7√3/2" makes no sense