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How do you graph #y=sec(1/4theta)#?

Answer 1

First, graph a #sec(theta)# graph: graph{sec(x) [-10, 10, -5, 5]} Then stretch the graph on the horizontal by a factor of 4: graph{sec(1/4x) [-10, 10, -5, 5]}

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Answer 2

Carter Anderson

To graph ( y = \sec\left(\frac{1}{4}\theta\right) ), follow these steps:

Identify the period of the function. For the secant function, the period is ( 2\pi ).
Determine the critical points where the function is undefined. Secant is undefined where its reciprocal function, cosine, equals zero. So, ( \cos\left(\frac{1}{4}\theta\right) = 0 ). Solve for ( \theta ) to find these critical points.
Plot the critical points on the graph.
Determine the behavior of the function between the critical points.
Sketch the graph, ensuring it repeats every ( 2\pi ) interval.

It's important to note that the secant function's graph will have asymptotes where the cosine function is zero. These asymptotes occur at regular intervals of ( \pi ) on the graph.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.