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Determine the number of different values that
/_x could be based on the given information.

sin x=0.4048
3
0
1
2

Determine the number of different values that $\angle x$ could be based on the given information. $\newline$ $\sin x=0.4048$ $\newline$ $3$ $\newline$ $0$ $\newline$ $1$ $\newline$ $2$

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Multiply radical expressions

Full solution

Q. Determine the number of different values that

\angle x

could be based on the given information.

\newline

\sin x=0.4048

\newline

3

\newline

0

\newline

1

\newline

2

Identify sine value: First, we know that $\sin x = 0.4048$ . The sine function is positive in the first and second quadrants.
Calculate reference angle: To find the reference angle, we use the inverse sine function on a calculator: $x = \sin^{-1}(0.4048)$ .
Determine angle in first quadrant: Calculating the reference angle gives us $x \approx 23.9$ degrees. This is the angle in the first quadrant.
Find angle in second quadrant: The second possible angle is in the second quadrant, which is $180 - 23.9$ degrees $= 156.1$ degrees.
Final possible values: So, there are two possible values for $\angle x$ : $23.9$ degrees and $156.1$ degrees.

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