Trigonometric Graphs Help! (1 Viewer)

[SGSII]

Hi Guys
Could someone please help explain how to sketch this graph:
y=1+sinx for 0≤x≤2π
Please help!
Thanks

 

[asianese]

Graph y=sinx first. Then shift your entire graph UP by 1 unit. You then have y=1+sinx.

 

[SGSII]

Thanks heaps!
Could someone please help me graph this one:
y=sin3x for 0≤x≤2π
And how do I work out how much to space out the x axis?

 

[Carrotsticks]

Thanks heaps!
Could someone please help me graph this one:
y=sin3x for 0≤x≤2π
And how do I work out how much to space out the x axis?

Graph the curve y=sin(x) as usual, from 0 to 2pi (space it out as usual too).

Then 'squish' everything so it's three times as 'squished'. So the X intercept at 0, pi and 2pi each become 0, pi/3 and 2pi/3 respectively.

But since we have to fill the domain, repeat your 'squished' curve another two times so it fills from 0 to 2pi.

 

[albertcamus]

It's the same as y = sinx except the period is 2pi/3 rad instead of being 2pi.

Just for rules basically: once you know how to sketch y = sinx, y = 2sinx simply doubles the amplitude, y = 3sinx triples the amplitude etc.

y = sin2x halves the period (2pi/2 which is just pi), y = sin5x makes the period equal 2pi/5 etc.

and to those equations above, if you add or minus a number to the equation e.g. y = sinx - 1 (y=sinx moved down by 1 unit) or y = sin2x + 3 (y= sin2x moved up by 3 units), it simply shifts the graph vertically up/down.

y = sin (x+1) moves y=sinx graph to the left by 1 unit etc.

 

[SGSII]

LOL thanks guys!