Trigonometric Graphs

Consider the function $f\left(x\right)=\csc x$`f`(`x`)=`c``s``c``x`, which is defined as the reciprocal function of $\sin x$`s``i``n``x`. That is, $\csc x=\frac{1}{\sin x}$`c``s``c``x`=1`s``i``n``x`.

a

Which of the following describes the values of $x$`x` where $\sin x=0$`s``i``n``x`=0?

$x=\pi n+\frac{\pi}{2}$`x`=π`n`+π2 where $n$`n` is an integer.

A

$x=2\pi n$`x`=2π`n` where $n$`n` is an integer.

B

$x=\pi n$`x`=π`n` where $n$`n` is an integer.

C

$x=\frac{\pi}{2}n$`x`=π2`n` where $n$`n` is an integer.

D

$x=\pi n+\frac{\pi}{2}$`x`=π`n`+π2 where $n$`n` is an integer.

A

$x=2\pi n$`x`=2π`n` where $n$`n` is an integer.

B

$x=\pi n$`x`=π`n` where $n$`n` is an integer.

C

$x=\frac{\pi}{2}n$`x`=π2`n` where $n$`n` is an integer.

D

b

What does your answer to part (a) imply about the function $f\left(x\right)=\csc x$`f`(`x`)=`c``s``c``x`?

$f\left(x\right)$`f`(`x`) is undefined when $x=\pi n$`x`=π`n`.

A

$f\left(x\right)$`f`(`x`) will reach its maximum value when $x=\pi n$`x`=π`n`.

B

$f\left(x\right)=0$`f`(`x`)=0 when $x=\pi n$`x`=π`n`.

C

$f\left(x\right)$`f`(`x`) will reach its minimum value when $x=\pi n$`x`=π`n`.

D

$f\left(x\right)$`f`(`x`) is undefined when $x=\pi n$`x`=π`n`.

A

$f\left(x\right)$`f`(`x`) will reach its maximum value when $x=\pi n$`x`=π`n`.

B

$f\left(x\right)=0$`f`(`x`)=0 when $x=\pi n$`x`=π`n`.

C

$f\left(x\right)$`f`(`x`) will reach its minimum value when $x=\pi n$`x`=π`n`.

D

Easy

Approx 2 minutes

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Display and interpret the graphs of functions with the graphs of their inverse and/or reciprocal functions