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

Understand Problem: Understand the problem and the range for θ. We need to express tan(174°) in terms of a different angle that is within the specified range of 0° to 360°. Since 174° is already within this range, we need to find an equivalent angle that has the same tangent value but is not 174° itself.Find Reference Angle: Find the reference angle for 174°. The reference angle is the acute angle formed by the terminal side of the given angle and the x-axis. Since 174° is in the second quadrant, its reference angle is 180° - 174° = 6°.Determine Equivalent Angle: Determine the equivalent angle with the same tangent value. The tangent function is positive in the first and third quadrants and negative in the second and fourth quadrants. Since 174° 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°.Express in terms of tan: Express tan(174°) in terms of tan(354°). Since tan(θ) = tan(θ + 180°) for all θ, and 174° and 354° differ by 180°, we have tan(174°) = tan(354°).

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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^{\circ} \leq \theta<360^{\circ} . $\newline$ $\tan \left(174^{\circ}\right)$ $\newline$ $\tan \left(\square^{\circ}\right)$

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Algebra 2

Find trigonometric ratios using reference angles

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Q. Express as a function of a DIFFERENT angle,

0^{\circ} \leq \theta<360^{\circ}

\newline

\tan \left(174^{\circ}\right)

\newline

\tan \left(\square^{\circ}\right)

Understand Problem: Understand the problem and the range for $\theta$ . We need to express $\tan(174^\circ)$ in terms of a different angle that is within the specified range of $0^\circ$ to $360^\circ$ . Since $174^\circ$ is already within this range, we need to find an equivalent angle that has the same tangent value but is not $174^\circ$ itself.
Find Reference Angle: Find the reference angle for $174°$ . The reference angle is the acute angle formed by the terminal side of the given angle and the x-axis. Since $174°$ is in the second quadrant, its reference angle is $180° - 174° = 6°$ .
Determine Equivalent Angle: Determine the equivalent angle with the same tangent value. $\newline$ The tangent function is positive in the first and third quadrants and negative in the second and fourth quadrants. Since $174^\circ$ 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 $360^\circ - 6^\circ = 354^\circ$ .
Express in terms of tan: Express $\tan(174°)$ in terms of $\tan(354°)$ . $\newline$ Since $\tan(\theta) = \tan(\theta + 180°)$ for all $\theta$ , and $174°$ and $354°$ differ by $180°$ , we have $\tan(174°) = \tan(354°)$ .