Express as a function of a DIFFERENT angle, 0^(@) <= theta < 360^(@). sin(218^(@)) sin(◻^(@))

Understand the problem: Understand the problem. We need to express sin(218°) as a function of a different angle, which is typically done by finding an equivalent angle within the standard range of 0° to 360° that has the same sine value.Find the reference angle: Find the reference angle. The reference angle is the acute angle that the given angle makes with the x-axis. Since 218° is in the third quadrant, we subtract it from 180° to find the reference angle. Reference angle = 218° - 180° = 38°.Determine equivalent angle: Determine the equivalent angle with the same sine value. Since sine is positive in the first and second quadrants, and 218° is in the third quadrant, we need to find an angle in the first or second quadrant that has the same sine value as 38°. The equivalent angle in the second quadrant is 180° - 38° = 142°.Express in terms of equivalent angle: Express sin(218°) in terms of the equivalent angle. We can now express sin(218°) as sin(142°) because they have the same sine value.

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Express as a function of a DIFFERENT angle,
0^(@) <= theta < 360^(@).

sin(218^(@))

sin(◻^(@))

Express as a function of a DIFFERENT angle, 0^{\circ} \leq \theta<360^{\circ} . $\newline$ $\sin \left(218^{\circ}\right)$ $\newline$ $\sin \left(\square^{\circ}\right)$

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Algebra 2

Find trigonometric ratios using reference angles

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Q. Express as a function of a DIFFERENT angle,

0^{\circ} \leq \theta<360^{\circ}

\newline

\sin \left(218^{\circ}\right)

\newline

\sin \left(\square^{\circ}\right)

Understand the problem: Understand the problem. $\newline$ We need to express $\sin(218^\circ)$ as a function of a different angle, which is typically done by finding an equivalent angle within the standard range of $0^\circ$ to $360^\circ$ that has the same sine value.
Find the reference angle: Find the reference angle. $\newline$ The reference angle is the acute angle that the given angle makes with the x-axis. Since $218°$ is in the third quadrant, we subtract it from $180°$ to find the reference angle. $\newline$ Reference angle = $218° - 180° = 38°$ .
Determine equivalent angle: Determine the equivalent angle with the same sine value. $\newline$ Since sine is positive in the first and second quadrants, and $218^\circ$ is in the third quadrant, we need to find an angle in the first or second quadrant that has the same sine value as $38^\circ$ . The equivalent angle in the second quadrant is $180^\circ - 38^\circ = 142^\circ$ .
Express in terms of equivalent angle: Express $\sin(218°)$ in terms of the equivalent angle. $\newline$ We can now express $\sin(218°)$ as $\sin(142°)$ because they have the same sine value.