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Express as a function of a DIFFERENT angle, 0^(@) <= theta < 360^(@). tan(174^(@)) tan(◻^(@))

Express as a function of a DIFFERENT angle, 0∘≤θ<360∘ 0^{\circ} \leq \theta<360^{\circ} .\newlinetan⁡(174∘) \tan \left(174^{\circ}\right) \newlinetan⁡(□∘) \tan \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} .\newlinetan⁡(174∘) \tan \left(174^{\circ}\right) \newlinetan⁡(□∘) \tan \left(\square^{\circ}\right)
  1. Understand Problem: Understand the problem and the range for θ\theta. We need to express tan⁡(174∘)\tan(174^\circ) in terms of a different angle that is within the specified range of 0∘0^\circ to 360∘360^\circ. Since 174∘174^\circ is already within this range, we need to find an equivalent angle that has the same tangent value but is not 174∘174^\circ itself.
  2. Find Reference Angle: Find the reference angle for 174°174°. The reference angle is the acute angle formed by the terminal side of the given angle and the x-axis. Since 174°174° is in the second quadrant, its reference angle is 180°−174°=6°180° - 174° = 6°.
  3. Determine Equivalent Angle: Determine the equivalent angle with the same tangent value.\newlineThe tangent function is positive in the first and third quadrants and negative in the second and fourth quadrants. Since 174∘174^\circ is in the second quadrant and we want a different angle, we can use the angle in the fourth quadrant that has the same reference angle, which is 360∘−6∘=354∘360^\circ - 6^\circ = 354^\circ.
  4. Express in terms of tan: Express tan⁡(174°)\tan(174°) in terms of tan⁡(354°)\tan(354°).\newlineSince tan⁡(θ)=tan⁡(θ+180°)\tan(\theta) = \tan(\theta + 180°) for all θ\theta, and 174°174° and 354°354° differ by 180°180°, we have tan⁡(174°)=tan⁡(354°)\tan(174°) = \tan(354°).

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