2sin(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.
sin(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.
sin(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.
- 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 or the altitude of the wave. The – sign in front of the tan graph also inverts the function about the x axis.
sin(x-30), cos(x-30), tan(x-30) The effect of the -30 is to shift the graph horizontally 30 0 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 30 0 in the negative direction (left). This has the same visual effect across sin, cos and tan.
Trig Graph Summary FunctionEffect 2sin(x), 2cos(x), 2tan(x)Twice as high sin(2x), cos(2x), tan(2x)Twice as frequent sin(x)+1, cos(x)+1, tan(x)+1Shift Vertically - sin(x), - cos(x), - tan(x)Invert sin(x-30), cos(x-30), tan(x-30)Shift Horiz (+left)(-right)