Question

Which of the following is the graph of y = sin(0.5x)?

Answer 1

You did not include the graphs, but I can explain how the graph is and so you can recognize it.


1) for x = 0, y = sin(0) = 0, so the  origin (0,0) is part of the graph.


2) The range of the function is the interval [-1, 1]. This is, y is from -1 to 1, and the graph oscilates (is a wave) between those minimum and maximum.


3) The periodicity, P, of the function is such that 0.5P = 2π = > P = 4π


That means that the values repeat every 4π interval (which is the same that 720°)


4) The zeroes of the function are 2π * n, where n is any whole number (negative, zero or positive).


That means that the function crosses the x-axis at

..., -6π, -4π, 2π, 0, 2π, 4π , 6π, ...


5) It is an odd function (which means that f(x) = sin(0.5x) = - f(-x) = - sin(-0.5x).


Now you have plenty information to identify the graph.

I also include a graph of the function in the attached pdf file.

Answer 2

The graph of y = sin (0.5x) can be seen in the picture in the attachment

Further explanation

Firstly , let us learn about trigonometry in mathematics.

Suppose the ΔABC is a right triangle and ∠A is 90°.

sin ∠A = opposite / hypotenuse

cos ∠A = adjacent / hypotenuse

tan ∠A = opposite / adjacent

There are several trigonometric identities that need to be recalled, i.e.

$cosec ~ A = \frac{1}{sin ~ A}$

$sec ~ A = \frac{1}{cos ~ A}$

$cot ~ A = \frac{1}{tan ~ A}$

$tan ~ A = \frac{sin ~ A}{cos ~ A}$

Let us now tackle the problem!

Given :

$y = \sin (0.5x)$

Let us try to find some important parameters of this function:

To find amplitude just look at the coefficient in front of the sine function which is 1, so the amplitude for this function is 1 unit.

y = 1 sin (0.5x)

To find the period, we will divide 2π by the coefficient of the variable x that is 0.5 in this function, so the period is 2π/0.5 = 4π

y = 1 sin (0.5x)

To find the maximum and minimum values, we substitute the maximum value of the sine function which is 1 and the minimum value of the sine function which is -1, so that the equation becomes:

Maximum Values of y = sin (0.5x) → y = 1

Minimum Values of y = sin (0.5x) → y = -1

From the values obtained above, a graph of the function can be sketched as shown in the picture in the attachment.

Learn more

• Calculate Angle in Triangle : https://brainly.com/question/12438587
• Periodic Functions and Trigonometry : https://brainly.com/question/9718382
• Trigonometry Formula : https://brainly.com/question/12668178

Answer details

Grade: College

Subject: Mathematics

Chapter: Trigonometry

Keywords: Sine , Cosine , Tangent , Opposite , Adjacent , Hypotenuse