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

Understand the problem: Understand the problem and the range of the angle. We need to express cos(130°) in terms of another angle that is within the range of 0° to 360°. We can use the concept of reference angles to find an equivalent expression for cos(130°).Find reference angle: Find the reference angle for 130°. The reference angle is the acute angle that the terminal side of the given angle makes with the x-axis. Since 130° is in the second quadrant, its reference angle is 180° - 130° = 50°.Determine cosine: Determine the cosine of the reference angle. The 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°).Express as function: Express cos(130°) as a function of a different angle. We can use the angle 50°, which is the reference angle, to express cos(130°) as -cos(50°). Alternatively, we can also use the angle 360° - 50° = 310°, which is in the fourth quadrant, to express cos(130°) as cos(310°) because cosine is positive in the fourth quadrant.

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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^{\circ} \leq \theta<360^{\circ} . $\newline$ $\cos \left(130^{\circ}\right)$ $\newline$ $\cos \left(\square^{\circ}\right)$

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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

\cos \left(130^{\circ}\right)

\newline

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

Understand the problem: Understand the problem and the range of the angle. $\newline$ We need to express $\cos(130^\circ)$ in terms of another angle that is within the range of $0^\circ$ to $360^\circ$ . We can use the concept of reference angles to find an equivalent expression for $\cos(130^\circ)$ .
Find reference angle: Find the reference angle for $130°$ . $\newline$ The reference angle is the acute angle that the terminal side of the given angle makes with the x-axis. Since $130°$ is in the second quadrant, its reference angle is $180° - 130° = 50°$ .
Determine cosine: Determine the cosine of the reference angle. $\newline$ The 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, $\cos(130^\circ) = -\cos(50^\circ)$ .
Express as function: Express $\cos(130°)$ as a function of a different angle. $\newline$ We can use the angle $50°$ , which is the reference angle, to express $\cos(130°)$ as $-\cos(50°)$ . Alternatively, we can also use the angle $360° - 50° = 310°$ , which is in the fourth quadrant, to express $\cos(130°)$ as $\cos(310°)$ because cosine is positive in the fourth quadrant.