# Write a sine function that has an amplitude of 4, a midline ofy =3 and a period of 37

**URL:** <https://sorumatik.co/t/write-a-sine-function-that-has-an-amplitude-of-4-a-midline-ofy-3-and-a-period-of-37/690201>\
**Category:** Maths Question\
**Created:** [Ağustos 16, 2026, 4:47öö UTC](https://sorumatik.co/t/write-a-sine-function-that-has-an-amplitude-of-4-a-midline-ofy-3-and-a-period-of-37/690201 "2026-08-16T04:47:04Z")\
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**Post date:** [Ağustos 16, 2026, 4:47öö UTC](https://sorumatik.co/t/write-a-sine-function-that-has-an-amplitude-of-4-a-midline-ofy-3-and-a-period-of-37/690201/1 "2026-08-16T04:47:04Z")

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Write a sine function that has an  
amplitude

of

4, a midline ofy =3

and a period of 37.  
Answer  
f(z) =  
Submit Answer

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**Author:** ![Sinav\_Rehberi](https://sorumatik.co/user_avatar/sorumatik.co/sinav_rehberi/32/154383_2.png) [@Sinav\_Rehberi](https://sorumatik.co/u/Sinav_Rehberi)\
**Post date:** [Ağustos 16, 2026, 4:47öö UTC](https://sorumatik.co/t/write-a-sine-function-that-has-an-amplitude-of-4-a-midline-ofy-3-and-a-period-of-37/690201/2 "2026-08-16T04:47:12Z")

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## Write a Sine Function with Amplitude 4, Midline y = 3, and Period 3\pi

💡 **FORMULA USED:**

The general equation for a standard sine function is:

f(x) = A \sin(Bx) + D

Where:

- |A| = Amplitude
- D = Vertical shift (Midline equation y = D)
- B = Frequency coefficient, related to the Period (P) by the formula:

\text{Period} = \frac{2\pi}{B} \implies B = \frac{2\pi}{\text{Period}}

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🧠 **SOLUTION STEPS:**

**Step 1 — Identify the Amplitude (A)**  
The problem states that the amplitude is 4.

A = 4

**Step 2 — Identify the Midline (D)**  
The midline is given as y = 3. This represents the vertical shift of the function.

D = 3

**Step 3 — Calculate the Frequency Coefficient (B)**  
The period of the function is given as 3\pi. Using the period formula B = \frac{2\pi}{\text{Period}}:

B = \frac{2\pi}{3\pi}

Cancel out \pi from the numerator and denominator:

B = \frac{2}{3}

**Step 4 — Assemble the Complete Function**  
Substitute A = 4, B = \frac{2}{3}, and D = 3 into the standard sine function equation f(x) = A \sin(Bx) + D:

f(x) = 4 \sin\left(\frac{2}{3}x\right) + 3

━━━━━━━━━━━━━━━━━━━━━━━━━━━  
✅ **ANSWER:**

f(x) = 4 \sin\left(\frac{2}{3}x\right) + 3

_(or written as `4 sin((2/3)x) + 3` for text input boxes)_  
━━━━━━━━━━━━━━━━━━━━━━━━━━━

🎯 **KEY CONCEPTS:**

**1. Amplitude (A)**

- **Definition:** The maximum distance the graph rises above or falls below its midline.
- **In this problem:** Determines the height of the peaks (4 units above and below the midline y = 3, reaching maximum y = 7 and minimum y = -1).

**2. Midline (D)**

- **Definition:** The horizontal reference axis y = D running midway between the maximum and minimum values of the trigonometric function.
- **In this problem:** Shifts the entire baseline of the graph up to y = 3.

**3. Period (P)**

- **Definition:** The horizontal length of one complete cycle of the wave before it repeats.
- **In this problem:** A full cycle completes every 3\pi units along the x-axis.

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⚠ **COMMON MISTAKES:**

**❌ Confusing Period with the Coefficient B**

- **Wrong:** Putting the period directly into the function: f(x) = 4 \sin(3\pi x) + 3.
- **Right:** Calculating B = \frac{2\pi}{\text{Period}} = \frac{2}{3} first, yielding f(x) = 4 \sin\left(\frac{2}{3}x\right) + 3.
- **Why it’s wrong:** The term inside the sine function represents angular frequency (B), not the period length itself.

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Would you like me to generate a similar practice problem with a phase shift to help you master transformed sine functions?