How would I graph this ?

Question

I know its kinda hard to show me how to do this. The problem says graph the two functions on the same coordinate planes (include two full periods)

f(x)= -1/2 sin x/2

g(x)= 3 - 1/2 sin x/2

well i forgot how to find the period, and the way to number the x axis. all the stuff involved in finding out how to graph the equations

Answer 1

ok. the first negative tells you that the sine wave goes below the x axis as opposed to above it first. The 1/2 means that instead of going to max of 1 and min of -1 its max is 1/2 and min -1/2. Usually on a sine graph when y = sin x there is a hill shape over the x axis and another under but as it is x/2, there is only one long bump for 360 degrees.

So basically the shape looks like a really shallow curve that goes below the x axis going down to -1/2. the end of the curve where it touches the x axis again should be at 360 degrees. for the second period just repeat only this time above the x axis and ending in 720.

For the second one, g(x), just slide the whole graph up three units.

If you are finding graphs difficult, i would suggest getting a graphic calculator. if you get the right one, you can even take it into the exam with you. they are quite expensive but worth the money.

Hope i helped :)

Answer 2

the regular finction of sinx starts at (0,0). has a maximum point at (pi/4,1) intersects the x axis at pi/2, has a minumum at (3pi/4, -1) and ends at (2pi,0). the period is 2pi and range is 1 to -1.

f(x) = a*sin(bx)

a = -1/2 and b =1/2

the period is 2pi/b

p = 2pi/(1/2) = 4pi

the range goes from positive a to negative a. since a is negative here, that means the graph will be flipped. instead of starting out going up, it will start going down.

this graph would act like this:

starts at (0,0) minimum at (pi,-1/2), cross x axis at 2pi, maximum at (3pi, 1/2) and end at (4pi,0).

g(x) is just 3 - f(x)

that mean f(x) becomes negative and add 3.

when you make a grpah negative, you flip it over the x axis. [like we did earlier]. so now f(x) = 1/2 sin x/2. and when you add 3, you move the whole graph 3 units up. so the start point moves from (0,0) to (0,3).

Answer 3

x  is the angle measured in radians. The period is the number of radians in one cycle, which is 4π.

The two curves have the same phase, period, and amplitude, but are offset by 3.

http://www.flickr.com/photos/dwread/2787...

Answer 4

the normal sine curve y=sinx, starts at (0,0) goes up to (pi/2,1), down to (pi, 0) then (3pi/2, -1) and back up to (2pi, 0) that is one period.

f(x) has a period of 2pi / (1/2) =4pi

it has an amplitude of 1/2 and goes down first since it is negative.

so you have (0,0), (pi, -1/2), (2pi,0), (3pi, 1/2), (4pi,0) then repeat out to (8pi,0)

g(x) is the same as f(x) but all the y values are raised by 3:

(3,0) (pi, 2 1/2) etc.

Answer 5

substitute values of x from 0 to 4pie with a spacing of pie/2 in f(x) and g(x) and plot points for each corresponding valve.

Answer 6

Period of f(x) = 4π,  [2π / (1/2)]

Now to number the x-axis mark the points π , 2π , 3π, 4π , and so on, [keep on adding π].

Now draw the graph as usually of the inverted sine curve (mirrored at x axis, because amplitude is negetive),  keep its amplitude 1/2.

Similarly the second one but after doing the above steps except to draw, draw such that it is shifted up ( vertically shifted) by 3 units.

Answer 7

assume a value for x

then  solve for the f(x) and g(x)

f(x) and g(x) are both in the y-axis

x, of course, in the x-axis