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

cos(5^(@))

cos(◻^(@))

Express as a function of a DIFFERENT angle, 0^{\circ} \leq \theta<360^{\circ} .\newlinecos(5) \cos \left(5^{\circ}\right) \newlinecos() \cos \left(\square^{\circ}\right)

Full solution

Q. Express as a function of a DIFFERENT angle, 0θ<360 0^{\circ} \leq \theta<360^{\circ} .\newlinecos(5) \cos \left(5^{\circ}\right) \newlinecos() \cos \left(\square^{\circ}\right)
  1. Understand co-terminal angles: Understand the concept of co-terminal angles. Co-terminal angles are angles that share the same initial and terminal sides. An angle's co-terminal can be found by adding or subtracting multiples of 360360^\circ (for degrees) or 2π2\pi (for radians).
  2. Find co-terminal angle: Find a co-terminal angle of 5° that is within the range 0° \leq \theta < 360°.\newlineSince 5° is already within the given range, we can find a co-terminal angle by adding 360°360° to 5°.\newlineCo-terminal angle = 5°+360°=365°5° + 360° = 365°
  3. Express in terms of cos: Express cos(5°)\cos(5°) in terms of cos(365°)\cos(365°).\newlineSince cos(θ)=cos(θ+360°n)\cos(\theta) = \cos(\theta + 360°n), where nn is an integer, we can express cos(5°)\cos(5°) as cos(365°)\cos(365°).
  4. Verify range: Verify that the new expression is within the range. \newline365365^\circ is not within the range 0^\circ \leq \theta < 360^\circ, so we cannot use it as the final answer. We need to find a different expression that is within the range.
  5. Use angle identities: Use angle identities to express cos(5)\cos(5^\circ) in terms of a different angle.\newlineWe can use the identity cos(θ)=cos(θ)\cos(\theta) = \cos(-\theta) to find a different expression for cos(5)\cos(5^\circ). This identity allows us to use the negative of the angle, which is within the range.\newlinecos(5)=cos(5)\cos(5^\circ) = \cos(-5^\circ)
  6. Verify new expression: Verify that the new expression is within the range.\newline5°-5° is within the range 0° \leq \theta < 360° because when we add 360°360° to 5°-5°, we get 355°355°, which is within the range.\newlinecos(5°)=cos(355°)\cos(5°) = \cos(355°)

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