Answer: To draw the graphs of the sine, cosine, and tangent functions, you can use the following steps:
Determine the period: The period of the function is the length of one complete cycle of the function. For the sine and cosine functions, the period is 2π, while for the tangent function, the period is π.
Determine the amplitude: The amplitude of the function is the distance between the maximum and minimum values of the function. For the sine and cosine functions, the amplitude is 1, while for the tangent function, there is no amplitude.
Determine the intercepts: The sine and tangent functions have x-intercepts at 0 and at multiples of the period, while the cosine function has x-intercepts at multiples of half the period. The sine and cosine functions have y-intercepts at 0, while the tangent function has a vertical asymptote at 0.
Plot the points: Plot points on the graph of the function at the x-intercepts, y-intercept, and other important points.
Sketch the curve: Use the points to sketch the curve of the function, following the general shape of the function and the periodicity.
Here are the graphs of the sine, cosine, and tangent functions:
Sine function:
The graph of the sine function oscillates between -1 and 1, and it crosses the x-axis at multiples of π.
The graph starts at (0, 0) and goes through a maximum at (π/2, 1), a minimum at (3π/2, -1), and another maximum at (5π/2, 1).
The period of the sine function is 2π.
Cosine function:
The graph of the cosine function oscillates between -1 and 1, and it crosses the x-axis at multiples of π/2.
The graph starts at (0, 1) and goes through a minimum at (π, -1), and then returns to its starting point at (2π, 1).
The period of the cosine function is 2π.
Tangent function:
The graph of the tangent function has vertical asymptotes at odd multiples of π/2, and it oscillates between positive and negative infinity.
The graph starts at (0, 0), has a vertical asymptote at π/2, crosses the x-axis at π, has another vertical asymptote at 3π/2, and returns to (0, 0) after crossing the x-axis at 2π.
The period of the tangent function is π.
Explanation: