Describe how the graph of each function is related to a basic trigonometric graph. then, graph two periods.

1. y=0.5 cos(3x) description:

2. y=-2 sin(2πx/3) description:

3. y=4 sin(3πx)-2 description:

QUESTION 1

The given trigonometric function is

The amplitude of this function is 0.5 while the amplitude of the parent function is 1.

The period of this function is while the parent function is

This function will complete two periods on the interval

We plot some few points as shown on the graph and draw our curve through it.

QUESTION 2

The given function is

This function has a period of 3 while the corresponding basic function, has a period of  

The amplitude of this function is 2 while that of the corresponding basic function is 1.

This function is reflected in the x-axis because of the negative a value.

We plot some few points and draw the graph as shown in the graph

QUESTION 3

The given function is

This function has an amplitude of 4 as compared to the amplitude of the basic sine which is 1.

It has a period of and shifted vertically 2 units down.

We plot some few points as shown in  the graph and draw our graph through.

$12. that is my answer.

5x + 3y = - 4

step-by-step explanation:

the equation of a line in standard form is

ax + by = c ( a is a positive integer and b, c are integers )

express the line first of all in slope- intercept form

y = mx + c ( m is the slope and c the y-intercept )

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (7, - 3) and (x₂, y₂ ) = (4, - 8)

m = = -

y = - x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (4, - 8 ), then

- 8 = - + c ⇒ c = -

y = - x - ← in slope-intercept form

multiply all terms by 3 to eliminate the fractions

3y = - 5x - 4 ( add 5x to both sides )

5x + 3y = - 4 ← in standard form