Question

In: Advanced Math

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

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

f(x) = tan x

Expert Solution

Consider the following trigonometric function:

f(x) = tanx

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

Put x = π/3 in the above function,

f(-π/3) = tan(-π/3)

= -tan(π/3)

= -√3

= -1.732

Put x = π/4 in the above function,

f(-π/4) = tan(-π/4)

= -tan(π/4)

= -1

Put x = 0 in the above function,

f(0) = tan(0)

= 0

Put x = π/6 in the above function,

f(π/6) = tan(π/6)

= 1/√3

= 0.5774

Put x = π/4 in the above function,

f(π/4) = tan(π/4)

= 1

Put x = π/3 in the above function,

f(π/3) = tan(π/3)

= √3

= 1.732

Now draw the table for the above values of function,

x	-π/3	-π/4	0	π/6	π/4	π/3
f(x)	-√3	-1	0	1/√3	1	√3

Now plot the graph with the table,

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

f(x) = tanx.

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

f(x) = tanx.

Junaid answered 1 year ago

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

For the following exercises, determine whether or not the given function f is continuous everywhere...f(x) = tan(x) + 2

For the following exercises, determine whether or not the given function f is continuous everywhere. If it is continuous everywhere it is defined, state for what range it is continuous. If it is discontinuous, state where it is discontinuous.f(x) = tan(x) + 2

Consider the function f(x)= tan 1/x Use the following table to guess the limit f(x) as...

Consider the function f(x)= tan 1/x Use the following table to guess the limit f(x) as x goes to 0+ x f(x) = tan 1/x 1/π 1/2π 1/3π 1/4π 1/5π 4/π 4/5π 4/9π 4/13π 4/17π

1-Use the (x,y) coordinates in the figure to find the value of the trigonometric function at...

1-Use the (x,y) coordinates in the figure to find the value of the trigonometric function at the indicated real number, t, or state that the expression is undefined. SIN 11π/6 2-Use the (x,y) coordinates in the figure to find the value of the trigonometric function at the indicated real number, t, or state that the expression is undefined. COS π//6 3- Use the (x,y) coordinates in the figure to find the value of tan 4π/3 or state that the expression...

For each of the following integrals find an appropriate trigonometric substitution of the form x=f(t)x=f(t) to...

For each of the following integrals find an appropriate trigonometric substitution of the form x=f(t)x=f(t) to simplify the integral. the inteagral a) ∫x(3x^2+30x+73)^(1/2)dx b)∫x/(−25−3x^2+18x)^(1/2)dx

For the following exercises, describe the end behavior of the graphs of the functions. f(x) = −5(4)x − 1

For the following exercises, describe the end behavior of the graphs of the functions.f(x) = −5(4)x − 1

For the following exercises, use the graphs shown in Figure 13. All have the form f(x) = abx . Which graph has the largest value for a?

For the following exercises, use the graphs shown in Figure 13. All have the form f(x) = abx .Which graph has the largest value for a?

For the following exercises, use the definition of derivative to calculate the derivative of each function. f(x) = 5π

For the following exercises, use the definition of derivative to calculate the derivative of each function.f(x) = 5π

For the following exercises, consider the function shown in Figure 17. At what x-coordinates is the function discontinuous?

For the following exercises, consider the function shown in Figure 17.At what x-coordinates is the function discontinuous?

For the following exercises, determine whether or not the given function f is continuous everywhere...f(x) = log2 (x)

For the following exercises, determine whether or not the given function f is continuous everywhere. If it is continuous everywhere it is defined, state for what range it is continuous. If it is discontinuous, state where it is discontinuous.f(x) = log2 (x)