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**Trig Graphs Investigate the effects of 2sin(x), 2cos(x), 2tan(x)**

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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.

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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.

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**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.

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**- 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.

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**sin(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.

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**Trig Graph Summary Function Effect**

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)+1 Shift Vertically - sin(x), - cos(x), - tan(x) Invert sin(x-30), cos(x-30), tan(x-30) Shift Horiz (+left)(-right)

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