Question

Algebra 2, please help! thank you

Answer 1

Answer:

-2pi/3

Step-by-step explanation:

y = 2 cos 3(x + 2π∕3) +1

y = A sin(B(x + C)) + D  

amplitude is A

period is 2π/B

phase shift is C (positive is to the left)

vertical shift is D

We have a shift to the left of 2 pi /3

Answer 2

Answer:

A

Step-by-step explanation:

The standard cosine function has the form:

$\displaystyle y = a\cos (b(x-c)) + d$

Where |a| is the amplitude, 2π / b is the period, c is the phase shift, and d is the vertical shift.

We have the function:

$\displaystyle y = 2 \cos 3\left(x + \frac{2\pi}{3}\right) + 1$

We can rewrite this as:

$\displaystyle y = \left(2\right)\cos 3\left(x - \left(-\frac{2\pi}{3}\right)\right) + 1$

Therefore, a = 2, b = 3, c = -2π/3, and d = 1.

Our phase shift is represented by c. Thus, the phase shift is -2π/3.

Our answer is A.