Find an equation to match graph ### Understanding Sine Wave GraphsThe graph displayed above represents a sine wave, a type of trigonometric function which is very important in mathematics, physics, and engineering due to its properties and applications in modeling periodic phenomena.#### Graph Details:1. **Axes:** - The horizontal axis (x-axis) represents the angle in radians. - The vertical axis (y-axis) represents the amplitude, or the value of the sine function at each given angle.2. **Grid:** - The graph is overlaid with a grid that helps in visualizing and identifying the coordinates of the points where the sine wave intersects the grid lines.3. **Sine Wave:** - The sine wave (in blue) oscillates above and below the x-axis. - The wave starts at a point above the x-axis, indicating a positive value (approximately at 6) and then proceeds to oscillate through multiple points. - The wave has a periodic nature meaning it repeats after each interval. - Key points of the wave in this graph are: - $ \frac{\pi}{2} $, where the sine function reaches its maximum value. - $ \pi $, where the sine function crosses the x-axis and becomes negative. - $ \frac{3\pi}{2} $, where it reaches its minimum value. - $ 2\pi $, where it crosses back to positive and this sets the wave to repeat. 4. **Tick Marks and Labels:** - The x-axis is marked at special intervals, specifically $ \frac{\pi}{4} $, $ \frac{\pi}{2} $, $ \frac{3\pi}{4} $, $ \pi $, and $ \frac{5\pi}{4} $, helping to identify key points in the wave's cycle.5. **Amplitude and Period:** - The amplitude of the sine wave (height from the center line to the peak) seems to be approximately 2 (from 6 to 8). - Each full cycle of the sine wave (from 0 to $ 2\pi $) represents one period.This graph helps in understanding how the sine function behaves over different intervals and demonstrates key properties such as its periodicity, amplitude, and zero-crossings. The sine function is fundamental to wave theory, alternating current (AC) in electrical engineering, and

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Answered: Find an equation to match graph

Math

Trigonometry

Find an equation to match graph

Trigonometry (11th Edition)

11th Edition

ISBN:9780134217437

Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels

Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels

Chapter1: Trigonometric Functions

Section: Chapter Questions

Problem 1RE: 1. Give the measures of the complement and the supplement of an angle measuring 35°.

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Concept explainers

Family of Curves

A family of curves is a group of curves that are each described by a parametrization in which one or more variables are parameters. In general, the parameters have more complexity on the assembly of the curve than an ordinary linear transformation. These families appear commonly in the solution of differential equations. When a constant of integration is added, it is normally modified algebraically until it no longer replicates a plain linear transformation. The order of a differential equation depends on how many uncertain variables appear in the corresponding curve. The order of the differential equation acquired is two if two unknown variables exist in an equation belonging to this family.

XZ Plane

In order to understand XZ plane, it's helpful to understand two-dimensional and three-dimensional spaces. To plot a point on a plane, two numbers are needed, and these two numbers in the plane can be represented as an ordered pair (a,b) where a and b are real numbers and a is the horizontal coordinate and b is the vertical coordinate. This type of plane is called two-dimensional and it contains two perpendicular axes, the horizontal axis, and the vertical axis.

Euclidean Geometry

Geometry is the branch of mathematics that deals with flat surfaces like lines, angles, points, two-dimensional figures, etc. In Euclidean geometry, one studies the geometrical shapes that rely on different theorems and axioms. This (pure mathematics) geometry was introduced by the Greek mathematician Euclid, and that is why it is called Euclidean geometry. Euclid explained this in his book named 'elements'. Euclid's method in Euclidean geometry involves handling a small group of innately captivate axioms and incorporating many of these other propositions. The elements written by Euclid are the fundamentals for the study of geometry from a modern mathematical perspective. Elements comprise Euclidean theories, postulates, axioms, construction, and mathematical proofs of propositions.

Lines and Angles

In a two-dimensional plane, a line is simply a figure that joins two points. Usually, lines are used for presenting objects that are straight in shape and have minimal depth or width.

Question

Find an equation to match graph

### Understanding Sine Wave Graphs

The graph displayed above represents a sine wave, a type of trigonometric function which is very important in mathematics, physics, and engineering due to its properties and applications in modeling periodic phenomena.

#### Graph Details:

1. **Axes:**
- The horizontal axis (x-axis) represents the angle in radians.
- The vertical axis (y-axis) represents the amplitude, or the value of the sine function at each given angle.

2. **Grid:**
- The graph is overlaid with a grid that helps in visualizing and identifying the coordinates of the points where the sine wave intersects the grid lines.

3. **Sine Wave:**
- The sine wave (in blue) oscillates above and below the x-axis.
- The wave starts at a point above the x-axis, indicating a positive value (approximately at 6) and then proceeds to oscillate through multiple points.
- The wave has a periodic nature meaning it repeats after each interval.
- Key points of the wave in this graph are:
- $ \frac{\pi}{2} $, where the sine function reaches its maximum value.
- $ \pi $, where the sine function crosses the x-axis and becomes negative.
- $ \frac{3\pi}{2} $, where it reaches its minimum value.
- $ 2\pi $, where it crosses back to positive and this sets the wave to repeat.

4. **Tick Marks and Labels:**
- The x-axis is marked at special intervals, specifically $ \frac{\pi}{4} $, $ \frac{\pi}{2} $, $ \frac{3\pi}{4} $, $ \pi $, and $ \frac{5\pi}{4} $, helping to identify key points in the wave's cycle.

5. **Amplitude and Period:**
- The amplitude of the sine wave (height from the center line to the peak) seems to be approximately 2 (from 6 to 8).
- Each full cycle of the sine wave (from 0 to $ 2\pi $) represents one period.

This graph helps in understanding how the sine function behaves over different intervals and demonstrates key properties such as its periodicity, amplitude, and zero-crossings. The sine function is fundamental to wave theory, alternating current (AC) in electrical engineering, and

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