The number pi (π) is used to make the graph of all three functions. This is because we use the unit circle to find sine, cosine and tangent, and the circumference of a circle is always the length of the diameter multiplied by pi. The graphs of sine, cosine and tangent are all done in radians rather than degrees. Degrees are converted into radians by multiplying the number of the degree by π divided by 180 degrees. When drawing a graph of sine, cosine and tangent, we draw in terms of pi rather than numbers on the x-axis. Sine and cosine will have their x-axis drawn by replacing numbers 1, 2, 3, 4, and so on with π, 2π, 3π, 4π and so on. The x-axis of tangent will use fractions of pi and will be written in sequential order of π/2, π, 3π/2, 2π and so on. If you convert the degrees of a unit circle to radians, you will see that π/2 corresponds to 90 degrees, π corresponds with 180 degrees, 3π/2 corresponds with 270 degrees and 2π corresponds with 360 degrees. The y-axis of all three functions will be written in normal numerals.
Begin by drawing a graph line for the sine function. This will have the x-axis distributed over π, 2π and so on. The cross between the x and y-axis will still be zero, and the negative side will be a mirror of the positive, and will read from right to left as -π, -2π, etc. When graphing the "normal" sine function, we are graphing the equation y = sinO, where the theta (O) stands for some unknown angle. In y = sinO, the curves of the graph will never go above one or negative one on the y-axis. The peak of sineO will repeatedly be one and the trough will repeatedly be negative one. The curves of the graph will always go through the x-axis at -2π, -π, 0, π, 2π, and so on, in both directions. Knowing this, we can complete the curve of the graph by drawing small dots on the x-axis at each of these numbers. We can also draw small dots back and forth between one and negative one at the y-axis between each number at the x-axis. Complete the sine graph by connecting the dots to see the sine curve.
Cosine is drawn with the same x and y-axis as sine. The function for "normal" cosine is y = cosO. This is drawn very similarly to sine, in that it never goes above or below the one and negative one on the y-axis. The peak and trough will also continue to hit one and negative one, respectively. The difference between the graphs is that the peaks and troughs are directly above or below the x-axis at the points -2π, -π, 0, π, 2π, and so on, in both directions. The curve of the graph goes through the x-axis directly between each point. Draw dots at each of the peaks and troughs and directly between the numbers on the x-axis to connect and view the cosine curve.
Tangent is drawn very differently from sine and cosine. We number the x-axis of tangent differently than cosine. Begin the tangent graph by drawing an unnumbered y-axis. Draw an x-axis with the numbers π/2, π, 3π/2, 2π and so on, sequentially from left to right on the positive side and the numbers -π/2, -π, -3π/2, -2π and so on, sequentially from right to left on the negative side. The y = tanO graph uses asymptotes to separate the periodic curves of this graph. Asymptotes are lines that continually approach curves but never actually touch the curve. The tangent function curves on the y-axis with no real trough or peak for infinity between asymptotes. Draw dashed lines to represent asymptotes at -π/2, π/2, -3π/2, 3π/2 and so on, across the graph. Draw your first tangent curve by starting at the top of the y-axis, near the asymptote line of π/2. Curve down until you hit the zero at the x-axis. Then begin a mirrored curve down to the asymptote at -π/2. But remember to never actually touch the asymptote. Repeat these same curves at π and -π, by using those numbers as the zero and staying between the asymptote lines on either side.