lim_(x rarr(pi)/(4))csc(x)=? Choose 1 answer: (A) (sqrt2)/(2) (B) (sqrt3)/(2) (C) sqrt2 (D) The limit doesn't exist.

Find sin(π/4): We need to find the limit of csc(x) as x approaches π/4. The csc(x) function is the reciprocal of the sin(x) function, so csc(x) = 1/sin(x). Therefore, we need to find the value of sin(x) when x is π/4.Calculate csc(π/4): The value of sin(π/4) is a well-known trigonometric value. Since π/4 is an angle in the first quadrant where all trigonometric functions are positive, sin(π/4) = √2/2.Simplify csc(π/4): Now that we have the value of sin(π/4), we can find the value of csc(π/4) by taking the reciprocal of sin(π/4). So, csc(π/4) = 1/(√2/2).To simplify 1/(√2/2), we multiply the numerator and the denominator by √2 to get rid of the radical in the denominator. This gives us csc(π/4) = √2/(√2*√2/2) = √2/(2/2) = √2.

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lim_(x rarr(pi)/(4))csc(x)=?
Choose 1 answer:
(A)
(sqrt2)/(2)
(B)
(sqrt3)/(2)
(C)
sqrt2
(D) The limit doesn't exist.

$\lim _{x \rightarrow \frac{\pi}{4}} \csc (x)=?$ $\newline$ Choose $1$ answer: $\newline$ (A) $\frac{\sqrt{2}}{2}$ $\newline$ (B) $\frac{\sqrt{3}}{2}$ $\newline$ (C) $\sqrt{2}$ $\newline$ (D) The limit doesn't exist.

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Algebra 1

Domain and range of square root functions: equations

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\lim _{x \rightarrow \frac{\pi}{4}} \csc (x)=?

\newline

Choose

1

answer:

\newline

(A)

\frac{\sqrt{2}}{2}

\newline

(B)

\frac{\sqrt{3}}{2}

\newline

(C)

\sqrt{2}

\newline

(D) The limit doesn't exist.

Find $\sin(\frac{\pi}{4})$ : We need to find the limit of $\csc(x)$ as $x$ approaches $\frac{\pi}{4}$ . The $\csc(x)$ function is the reciprocal of the $\sin(x)$ function, so $\csc(x) = \frac{1}{\sin(x)}$ . Therefore, we need to find the value of $\sin(x)$ when $x$ is $\frac{\pi}{4}$ .
Calculate $\csc(\frac{\pi}{4})$ : The value of $\sin(\frac{\pi}{4})$ is a well-known trigonometric value. Since $\frac{\pi}{4}$ is an angle in the first quadrant where all trigonometric functions are positive, $\sin(\frac{\pi}{4}) = \frac{\sqrt{2}}{2}$ .
Simplify $\csc(\frac{\pi}{4})$ : Now that we have the value of $\sin(\frac{\pi}{4})$ , we can find the value of $\csc(\frac{\pi}{4})$ by taking the reciprocal of $\sin(\frac{\pi}{4})$ . So, $\csc(\frac{\pi}{4}) = \frac{1}{(\sqrt{2}/2)}$ .
Simplify $\csc(\frac{\pi}{4})$ : Now that we have the value of $\sin(\frac{\pi}{4})$ , we can find the value of $\csc(\frac{\pi}{4})$ by taking the reciprocal of $\sin(\frac{\pi}{4})$ . So, $\csc(\frac{\pi}{4}) = \frac{1}{(\sqrt{2}/2)}$ .To simplify $\frac{1}{(\sqrt{2}/2)}$ , we multiply the numerator and the denominator by $\sqrt{2}$ to get rid of the radical in the denominator. This gives us $\csc(\frac{\pi}{4}) = \frac{\sqrt{2}}{(\sqrt{2}*\sqrt{2}/2)} = \frac{\sqrt{2}}{(2/2)} = \sqrt{2}$ .