Express as a function of a DIFFERENT angle, 0^(@) <= theta < 360^(@). sin(344^(@)) sin(◻^(@))

Understand Period of Sine Function: Recognize that the sine function has a period of 360°, which means that sin(θ) = sin(θ + 360°k), where k is an integer. However, since we want to express sin(344°) as a function of a different angle within the range of 0° to 360°, we need to find an angle that is coterminal with 344° and falls within the specified range.Find Coterminal Angle: To find a coterminal angle that is within the range of 0° to 360°, we can subtract 360° from 344° if the angle is greater than 360°, or add 360° if the angle is less than 0°. Since 344° is less than 360°, we can find a coterminal angle by subtracting 344° from 360°.Calculate Coterminal Angle: Calculate the coterminal angle by subtracting 344° from 360°. 360° - 344° = 16° So, sin(344°) is equivalent to sin(360° - 16°), which is sin(16°) because sine is an odd function, and sin(-θ) = -sin(θ).Express as Different Angle: Since sin(344°) = sin(16°), we have expressed sin(344°) as a function of a different angle within the range of 0° to 360°.

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

sin(344^(@))

sin(◻^(@))

Express as a function of a DIFFERENT angle, 0^{\circ} \leq \theta<360^{\circ} . $\newline$ $\sin \left(344^{\circ}\right)$ $\newline$ $\sin \left(\square^{\circ}\right)$

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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(344^{\circ}\right)

\newline

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

Understand Period of Sine Function: Recognize that the sine function has a period of $360°$ , which means that $\sin(\theta) = \sin(\theta + 360°k)$ , where $k$ is an integer. However, since we want to express $\sin(344°)$ as a function of a different angle within the range of $0°$ to $360°$ , we need to find an angle that is coterminal with $344°$ and falls within the specified range.
Find Coterminal Angle: To find a coterminal angle that is within the range of $0^\circ$ to $360^\circ$ , we can subtract $360^\circ$ from $344^\circ$ if the angle is greater than $360^\circ$ , or add $360^\circ$ if the angle is less than $0^\circ$ . Since $344^\circ$ is less than $360^\circ$ , we can find a coterminal angle by subtracting $344^\circ$ from $360^\circ$ .
Calculate Coterminal Angle: Calculate the coterminal angle by subtracting $344^\circ$ from $360^\circ$ . $\newline$ $360^\circ - 344^\circ = 16^\circ$ $\newline$ So, $\sin(344^\circ)$ is equivalent to $\sin(360^\circ - 16^\circ)$ , which is $\sin(16^\circ)$ because sine is an odd function, and $\sin(-\theta) = -\sin(\theta)$ .
Express as Different Angle: Since $\sin(344°) = \sin(16°)$ , we have expressed $\sin(344°)$ as a function of a different angle within the range of $0°$ to $360°$ .