Question
2. (1 point) The first minimum along positive x-axis of y=2cos(3x) occurs at: x=90^circ x=60^circ x=0^circ d. x=180^circ
Solution
4.3
(224 Votes)
Elise
Professional ยท Tutor for 6 years
Answer
To determine the first minimum of the function \( y = 2 \cos(3x) \) along the positive
-axis, we need to analyze the behavior of the cosine function.---### Step 1: General form of cosine minimaThe cosine function \( \cos(kx) \) has minima when:
This occurs at:
where
is an integer. Solving for
, we get:
For our specific function \( y = 2 \cos(3x) \), the value of
. Therefore, the minima occur at:
---### Step 2: First minimum along the positive
-axisThe first minimum corresponds to
:
---### Step 3: Convert to degreesSince
radians equals
, we convert
to degrees:
---### Final Answer:The first minimum along the positive
-axis occurs at:
Correct option: **b.
**