Contents:

• The Graphs of Sin Cos and Tan:
  • Positive & Negative:

 

The Graphs of Sin Cos and Tan: Using 'y' for the vertical axis and 'x' for the horizontal axis, the curve y = sin x is basically the same as y = cos x. cos x is 90in advance of sin x, ie. the curve has advanced of the complete cycle along the 'x' axis. The limits on the 'y' axis are 1 and -1 and the graph repeats every 360.

The graph of y = tan x bears no resemblance to sin or cos.There are no limits at 90and at 270where the line goes to + infinity and - infinity. The tan graph repeats every 180.

The sine, cosine and tangent can be defined by using the co-ordinates on a circle, and apply to any size of angle. OP is the radius, of 1 unit of length. P has the co-ordinates (x, y).

Wherever P is on the circle it will make the anglewith the positive 'x' axis. The co-ordinates of P (x, y) will give the trigonometric ratios of .

Example: = 60,

therefore the length of x = cos 60 = = 05.

and the length of y = sin 60 = = 0866.

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Positive & Negative:

sin = y co-ordinate of P. Above the 'x' axis the number is positive, below the 'x' axis is negative.

        First Quadrant: positive, Second: positive, Third: negative, Fourth: negative.

cos = x co-ordinate of P. Right of the 'y' axis the number is positive, left of the 'y' axis is negative.

First Quadrant: positive, Second: negative, Third: negative, Fourth: positive.

tan = When both co-ordinates are positive or negative the number is positive.

First Quadrant: positive, Second: negative, Third: positive, Fourth: negative.

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