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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∘≤θ<360∘ 0^{\circ} \leq \theta<360^{\circ} .\newlinesin⁡(344∘) \sin \left(344^{\circ}\right) \newlinesin⁡(□∘) \sin \left(\square^{\circ}\right)

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Q. Express as a function of a DIFFERENT angle, 0∘≤θ<360∘ 0^{\circ} \leq \theta<360^{\circ} .\newlinesin⁡(344∘) \sin \left(344^{\circ}\right) \newlinesin⁡(□∘) \sin \left(\square^{\circ}\right)
  1. Understand Period of Sine Function: Recognize that the sine function has a period of 360°360°, which means that sin⁡(θ)=sin⁡(θ+360°k)\sin(\theta) = \sin(\theta + 360°k), where kk is an integer. However, since we want to express sin⁡(344°)\sin(344°) as a function of a different angle within the range of 0°0° to 360°360°, we need to find an angle that is coterminal with 344°344° and falls within the specified range.
  2. Find Coterminal Angle: To find a coterminal angle that is within the range of 0∘0^\circ to 360∘360^\circ, we can subtract 360∘360^\circ from 344∘344^\circ if the angle is greater than 360∘360^\circ, or add 360∘360^\circ if the angle is less than 0∘0^\circ. Since 344∘344^\circ is less than 360∘360^\circ, we can find a coterminal angle by subtracting 344∘344^\circ from 360∘360^\circ.
  3. Calculate Coterminal Angle: Calculate the coterminal angle by subtracting 344∘344^\circ from 360∘360^\circ. \newline360∘−344∘=16∘360^\circ - 344^\circ = 16^\circ\newlineSo, sin⁡(344∘)\sin(344^\circ) is equivalent to sin⁡(360∘−16∘)\sin(360^\circ - 16^\circ), which is sin⁡(16∘)\sin(16^\circ) because sine is an odd function, and sin⁡(−θ)=−sin⁡(θ)\sin(-\theta) = -\sin(\theta).
  4. Express as Different Angle: Since sin⁡(344°)=sin⁡(16°)\sin(344°) = \sin(16°), we have expressed sin⁡(344°)\sin(344°) as a function of a different angle within the range of 0°0° to 360°360°.

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