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Express as a function of a DIFFERENT angle, 0^(@) <= theta < 360^(@). cos(130^(@)) cos(◻^(@))

Express as a function of a DIFFERENT angle, 0∘≤θ<360∘ 0^{\circ} \leq \theta<360^{\circ} .\newlinecos⁡(130∘) \cos \left(130^{\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⁡(130∘) \cos \left(130^{\circ}\right) \newlinecos⁡(□∘) \cos \left(\square^{\circ}\right)
  1. Understand the problem: Understand the problem and the range of the angle.\newlineWe need to express cos⁡(130∘)\cos(130^\circ) in terms of another angle that is within the range of 0∘0^\circ to 360∘360^\circ. We can use the concept of reference angles to find an equivalent expression for cos⁡(130∘)\cos(130^\circ).
  2. Find reference angle: Find the reference angle for 130°130°.\newlineThe reference angle is the acute angle that the terminal side of the given angle makes with the x-axis. Since 130°130° is in the second quadrant, its reference angle is 180°−130°=50°180° - 130° = 50°.
  3. Determine cosine: Determine the cosine of the reference angle.\newlineThe cosine of the reference angle is the same as the absolute value of the cosine of the original angle, but we must consider the sign based on the quadrant. In the second quadrant, cosine is negative. Therefore, cos⁡(130∘)=−cos⁡(50∘)\cos(130^\circ) = -\cos(50^\circ).
  4. Express as function: Express cos⁡(130°)\cos(130°) as a function of a different angle.\newlineWe can use the angle 50°50°, which is the reference angle, to express cos⁡(130°)\cos(130°) as −cos⁡(50°)-\cos(50°). Alternatively, we can also use the angle 360°−50°=310°360° - 50° = 310°, which is in the fourth quadrant, to express cos⁡(130°)\cos(130°) as cos⁡(310°)\cos(310°) because cosine is positive in the fourth quadrant.

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