Answer:
The graph of each function is given below.
Explanation:
y = sin(x):
The graph of y = sin(x) represents the sine function.
The sine function is periodic with a period of 2π, meaning that it repeats itself every 2π units.
The graph oscillates between -1 and 1 as x increases.
y = cos(x):
The graph of y = cos(x) represents the cosine function.
Like the sine function, the cosine function is also periodic with a period of 2π.
However, the cosine function starts at its maximum value of 1 at x = 0.
As x increases, the graph moves downward until it reaches its minimum value of -1 at x = π/2.
It then starts increasing and reaches its maximum value of 1 again at
x = π.
The graph continues to oscillate between 1 and -1 as x increases further.
y = tan(x):
The graph of y = tan(x) represents the tangent function.
The tangent function is not periodic like sine and cosine.
It has vertical asymptotes (lines that the graph approaches but never crosses) at x = π/2, 3π/2, 5π/2, etc., where the function is undefined.
The graph has a repeating pattern of increasing and decreasing sections.
As x approaches the vertical asymptotes, the graph approaches positive or negative infinity.
y = cot(x):
The graph of y = cot(x) represents the cotangent function, which is the reciprocal of the tangent function.
Like the tangent function, the cotangent function also has vertical asymptotes at x = 0, π, 2π, etc.
It has a similar repeating pattern of increasing and decreasing sections as x approaches the vertical asymptotes.
Thus,
The graph of each function is given below.