Graphing sec/csc and tan/cot

Front

What is the equation of the secant function?

Back

y = sec(x) = 1/cos(x)

Front

How does the graph of y = sec(x) differ from y = cos(x)?

Back

The graph of y = sec(x) has vertical asymptotes where cos(x) = 0, and it opens upwards and downwards away from these asymptotes.

Front

What is the effect of adding a constant to the secant function, such as in y = sec(x) + 2?

Back

It shifts the graph of the secant function vertically by 2 units.

Front

What are the vertical asymptotes of the function y = sec(x)?

Back

The vertical asymptotes occur at x = (2n+1)π/2, where n is an integer.

Front

What is the parent function of the secant function?

Back

The parent function of the secant function is y = sec(x).

Front

What is the relationship between the tangent and cotangent functions?

Back

The cotangent function is the reciprocal of the tangent function: cot(x) = 1/tan(x).

Front

What are the vertical asymptotes of the function y = tan(x)?

Back

The vertical asymptotes occur at x = (2n+1)π/2, where n is an integer.

Front

What happens to the domain of the tangent function when it is vertically stretched?

Back

The domain remains the same; vertical stretching does not affect the domain.

Front

What is the equation for a vertically stretched tangent function, such as y = 2tan(x)?

Back

The equation y = 2tan(x) stretches the graph of y = tan(x) vertically by a factor of 2.

Front

How do you determine the period of the tangent function?

Back

The period of the tangent function is π.