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Express as a function of a DIFFERENT angle, 0^(@) <= theta < 360^(@). cos(154^(@)) cos(◻^(@))

Express as a function of a DIFFERENT angle, 0∘≤θ<360∘ 0^{\circ} \leq \theta<360^{\circ} .\newlinecos⁡(154∘) \cos \left(154^{\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⁡(154∘) \cos \left(154^{\circ}\right) \newlinecos⁡(□∘) \cos \left(\square^{\circ}\right)
  1. Find Reference Angle: We need to express cos⁡(154°)\cos(154°) in terms of a reference angle. A reference angle is the acute angle formed by the terminal side of an angle and the x-axis. The reference angle for any angle in the second quadrant, where 154°154° lies, is found by subtracting the angle from 180°180°.\newlineCalculation: 180°−154°=26°180° - 154° = 26°
  2. Use Even Property: The cosine function is even, which means that cos⁡(θ)=cos⁡(−θ)\cos(\theta) = \cos(-\theta). Therefore, cos⁡(154∘)\cos(154^\circ) can be expressed as cos⁡(180∘−26∘)\cos(180^\circ - 26^\circ), which is equivalent to −cos⁡(26∘)-\cos(26^\circ) because cosine is negative in the second quadrant.
  3. Express as −cos⁡(26°)-\cos(26°): We have now expressed cos⁡(154°)\cos(154°) as a function of a different angle, −cos⁡(26°)-\cos(26°), which is within the range 0°≤θ<360°0° \leq \theta < 360°.

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