Express as a function of a DIFFERENT angle, 0^(@) <= theta < 360^(@). tan(310^(@)) tan(◻^(@))

Understand the problem: Understand the problem. We need to express tan(310°) as a function of a different angle within the range of 0° to 360°. We can use the fact that the tangent function has a period of 180°, which means tan(θ) = tan(θ + 180°). We can also use the symmetry properties of the tangent function on the unit circle.Find the reference angle: Find the reference angle. The reference angle is the acute angle that the terminal side of the given angle makes with the x-axis. For an angle in the fourth quadrant, like 310°, the reference angle is 360° - 310° = 50°. This means tan(310°) is equal to tan(50°), but since 310° is in the fourth quadrant where tangent is negative, we have tan(310°) = -tan(50°).Express as a function: Express tan(310°) as a function of a different angle. We can use the reference angle found in Step 2 to express tan(310°) as a function of 50°. Since tan(θ) = -tan(180° - θ) for angles in the second quadrant, we can say tan(310°) = -tan(180° - 50°) = -tan(130°). Therefore, tan(310°) can be expressed as -tan(130°).

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

tan(310^(@))

tan(◻^(@))

Express as a function of a DIFFERENT angle, 0^{\circ} \leq \theta<360^{\circ} . $\newline$ $\tan \left(310^{\circ}\right)$ $\newline$ $\tan \left(\square^{\circ}\right)$

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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(310^{\circ}\right)

\newline

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

Understand the problem: Understand the problem. $\newline$ We need to express $\tan(310°)$ as a function of a different angle within the range of $0°$ to $360°$ . We can use the fact that the tangent function has a period of $180°$ , which means $\tan(\theta) = \tan(\theta + 180°)$ . We can also use the symmetry properties of the tangent function on the unit circle.
Find the reference angle: Find the reference angle. $\newline$ The reference angle is the acute angle that the terminal side of the given angle makes with the x-axis. For an angle in the fourth quadrant, like $310^\circ$ , the reference angle is $360^\circ - 310^\circ = 50^\circ$ . This means $\tan(310^\circ)$ is equal to $\tan(50^\circ)$ , but since $310^\circ$ is in the fourth quadrant where tangent is negative, we have $\tan(310^\circ) = -\tan(50^\circ)$ .
Express as a function: Express $\tan(310°)$ as a function of a different angle. $\newline$ We can use the reference angle found in Step $2$ to express $\tan(310°)$ as a function of $50°$ . Since $\tan(\theta) = -\tan(180° - \theta)$ for angles in the second quadrant, we can say $\tan(310°) = -\tan(180° - 50°) = -\tan(130°)$ . Therefore, $\tan(310°)$ can be expressed as $-\tan(130°)$ .