Question

In: Advanced Math

For the following exercises, match each trigonometric function with one of the graphs in Figure 18. f(x) = sec x

For the following exercises, match each trigonometric function with one of the graphs in Figure 18.

f(x) = sec x

Expert Solution

Consider the following trigonometric function:

f(x) = secx

The above equation is reciprocal of cosine function, so the function can be rewritten as,

f(x) = 1/cosx

To acknowledge the graph among the provided graphs in textbook, first sketch the graph of above function,

Put x = 0 in the above function,

f(0) = 1/cox(0)

= 1/1

= 1

Put x = π/4 in the above function,

f(π/4) = 1/cos(π/4)

= 1/(1/√2)

= √2

Put x = π/3 in the above function,

f(π/3) = 1/cos(π/3)

= 1/(1/2)

= 2

Put x = 2π/3 in the above function,

f(2π/3) = 1/cos(2π/3)

= 1/(-1/2)

= -2

Put x = π in the above function,

f(π) = 1/cosπ

= 1/(-1)

= -1

Now draw the table for the above values of function,

x	0	π/4	π/3	2π/3	π
f(x)	1	√2	2	-2	-1

Now plot the graph with the table,

Hence it is cleared that the graph IV provided in the textbook is the graph of the function

f(x) = secx.

Hence it is cleared that the graph IV provided in the textbook is the graph of the function

f(x) = secx.

Junaid answered 1 year ago

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