Identify the beginning of a sample period for he function:

Question

f(t) = 4sec(3t −6π)

 

a. x=2pi

b. x=1

c. x=2pi/3

d. x=pi

Answer 1

See the following method for the solution. I have simplified this problem in two steps. Follow these steps to find the beginning of the period for any function.

f(t) = 4sec(3t-6π)

STEP 1: FIND THE ARGUMENT OF THE FUNCTION

- The argument here is (3t-6π).

STEP 2: SET THE ARGUMENT = 0, AND SOLVE FOR "t"

- 3t - 6π = 0

- 3t - 6π + 6π = 6π (add 6π to both sides)

- 3t = 6π (simplify the equation)

- 3t/3 = 6π/3 (divide both sides of the equation by 3)

- t = 2π (simplify the equation)

Thus, t = 2π is the beginning of the period.

Answer 2

The secant function has the same period as the cosine function, which is 2π. The coefficient 3 inside the argument modifies the period. The formula for the new period is Period = 2π / B, where B = 3. The period now becomes 2π / 3. To find the beginning of a period, solve 3t - 6π = 0, as this corresponds to the start of the cycle. Solving 3t - 6π = 0 gives 3t = 6π, so t = 2π. The beginning of the period is t = 2π. The correct answer is x = 2π.

Answer 3

Identify the beginning of a sample period for the function: f (t) = f sec (3t-6pi)

Multiple Choice

a. x = 2pi

b. x = 1

c. x = 2pi divided by 3

d. x = pi

To find the beginning of a sample period for the function f(t)= sec(3t - 6 pi) implement the following steps:

Identify the function frequency. The function is in the form sec (k x t) sec (3t - 6 pi) k= 3

The beginning of the sample period starts at t = 0.

3t - 6π = 0

Solve for t:

To solve for t in the equation 3t−6π = 0, follow these steps:

3t - 6π = 0

Add 6π to both sides

3t = 6π

Divide both sides by 3:

t= 6π divided by 3

Simplify the fraction

t = 6π divided by 3

t = 2π

So, the answer is t=2π or Choice a. x = 2π

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I hope the mathematical calculations (step by step approach) was helpful. Please let me know if you require any more assistance. If anyone in my neighborhood is interested in setting up an in-person math tutoring session. I look forward to hearing from them. Have an amazing day. Doris H.