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Express as a function of a DIFFERENT angle, 0^(@) <= theta < 360^(@). cos(308^(@)) cos(◻^(@))

Express as a function of a DIFFERENT angle, 0∘≤θ<360∘ 0^{\circ} \leq \theta<360^{\circ} .\newlinecos⁡(308∘) \cos \left(308^{\circ}\right) \newlinecos⁡(□∘) \cos \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} .\newlinecos⁡(308∘) \cos \left(308^{\circ}\right) \newlinecos⁡(□∘) \cos \left(\square^{\circ}\right)
  1. Understand concept reference angles: Understand the concept of reference angles. The reference angle is the acute angle that a given angle makes with the x-axis. It is always between 0∘0^\circ and 90∘90^\circ and can be used to find the cosine of the original angle because cosine is the x-coordinate on the unit circle.
  2. Find reference angle 308°308°: Find the reference angle for 308°308°. Since 308°308° is in the fourth quadrant (where angles are between 270°270° and 360°360°), we subtract it from 360°360° to find the reference angle. Reference angle = 360°−308°=52°360° - 308° = 52°
  3. Determine cosine reference angle: Determine the cosine of the reference angle.\newlineThe cosine of an angle in the fourth quadrant is positive, and since the reference angle is 52∘52^\circ, we have:\newlinecos⁡(52∘)=cos⁡(360∘−308∘)\cos(52^\circ) = \cos(360^\circ - 308^\circ)
  4. Express cosine function: Express the original cosine function in terms of the reference angle.\newlineSince the cosine function is positive in the fourth quadrant, we can write:\newlinecos⁡(308°)=cos⁡(360°−52°)=cos⁡(52°)\cos(308°) = \cos(360° - 52°) = \cos(52°)

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