Presentation on theme: "Trig Graphs Investigate the effects of 2sin(x), 2cos(x), 2tan(x)"— Presentation transcript:
1Trig Graphs Investigate the effects of 2sin(x), 2cos(x), 2tan(x)
22sin(x), 2cos(x), 2tan(x)The 2sin(x) and 2cos(x) graphs are obviously twice as high, but still centred around the x-axis.The 2tan(x) graph does not show as marked a difference, but does appear slightly steeper.
3sin(2x), cos(2x), tan(2x)Sin(x) and Cos(x) both complete a cycle in 360 degrees.Sin(2x) and Cos(2x) both complete a cycle in 180 degrees.The amplitude remains the same.The (2x) completes a cycle in 1/2 the time, while (3x) completes in 1/3 the time.Tan(x) completes a cycle in 180 degrees.Tan(2x) completes a cycle in 90 degrees.
4sin(x)+1, cos(x)+1, tan(x)+1 The sin(x)+1 and cos(x)+1 graphs are moved vertically by 1.If the sign is negative, the graph would be moved down by that amount.Adding +1 and moving the tan graph up by 1 appears to make little difference.
5- sin(x), - cos(x), - tan(x) The – sign in front of the sin or cos graph inverts the graph about the x axis, but does not alter the number of waves in 3600 or the altitude of the wave.The – sign in front of the tan graph also inverts the function about the x axis.
6sin(x-30), cos(x-30), tan(x-30) The effect of the -30 is to shift the graph horizontally 300 in the opposite direction to what would seem logical i.e. positive(right).If the function was sin(x+30) then the graph would be shifted by 300 in the negative direction (left).This has the same visual effect across sin, cos and tan.