The graph of 𝑦=𝐴cos⁡(𝐵𝑥+𝐶) has a phase shift of 𝐶𝐵.Group of answer choicesTrueFalse

Step 1: Break Down the Problem

We need to determine if the phase shift of the function $y = A \cos(Bx + C)$ is equal to $\frac{C}{B}$.

Step 2: Relevant Concepts

The general form of a cosine function is given as: $y = A \cos(Bx + C)$ The phase shift of a cosine function can be calculated using the formula: $\text{Phase Shift} = -\frac{C}{B}$

Step 3: Analysis and Detail

1. The term $C$ in the function represents a horizontal shift. The value of $B$ affects the period of the cosine function.
2. To find the actual phase shift, we calculate $-\frac{C}{B}$.
3. The expression $\frac{C}{B}$ indicates that the shift is in the opposite direction of $C$. Therefore, the statement that the phase shift is $\frac{C}{B}$ is incorrect, as the correct phase shift is actually $-\frac{C}{B}$.

Step 4: Verify and Summarize

From our calculations and understanding, the phase shift is given by $-\frac{C}{B}$, confirming that the statement is false.

Final Answer

False. The phase shift of $y = A \cos(Bx + C)$ is $-\frac{C}{B}$, not $\frac{C}{B}$.