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

sin x=0.7896
0
1
3
2

Determine the number of different values that $\angle x$ could be based on the given information. $\newline$ $\sin x=0.7896$ $\newline$ $0$ $\newline$ $1$ $\newline$ $3$ $\newline$ $2$

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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=0.7896

\newline

0

\newline

1

\newline

3

\newline

2

Identify Quadrant: $\sin x = 0.7896$ means $x$ is in the first or second quadrant because sine is positive in these quadrants.
Find Reference Angle: To find the reference angle, we use the inverse sine function: $x = \arcsin(0.7896)$ .
Calculate First Value: Using a calculator, we find the reference angle to be approximately $x \approx 52.06$ degrees.
Calculate Second Value: The first value of $x$ is in the first quadrant, so $x \approx 52.06$ degrees.
Calculate Second Value: The first value of $x$ is in the first quadrant, so $x \approx 52.06$ degrees.The second value of $x$ is in the second quadrant. To find it, we subtract the reference angle from $180$ degrees: $180 - 52.06 = 127.94$ degrees.
Calculate Second Value: The first value of $x$ is in the first quadrant, so $x \approx 52.06$ degrees.The second value of $x$ is in the second quadrant. To find it, we subtract the reference angle from $180$ degrees: $180 - 52.06 = 127.94$ degrees.Therefore, there are $2$ different values that $\angle x$ could be.

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