Math / Trigonometry

QuestionFind the reference angle for 192 degrees.

Studdy Solution

STEP 1

1. A reference angle is the smallest angle that the terminal side of a given angle makes with the x-axis.
2. Reference angles are always positive and less than or equal to $90^\circ$ .

STEP 2

1. Determine the quadrant in which the angle lies.
2. Calculate the reference angle.

STEP 3

First, determine the quadrant for the angle $192^\circ$ . Angles between $180^\circ$ and $270^\circ$ lie in the third quadrant.

STEP 4

In the third quadrant, the reference angle is found by subtracting $180^\circ$ from the given angle. This is because the reference angle is the angle between the terminal side and the negative x-axis.

STEP 5

Calculate the reference angle:
$192^\circ - 180^\circ = 12^\circ$
The reference angle for $192^\circ$ is:
$\boxed{12^\circ}$

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QuestionFind the reference angle for 192 degrees.

Studdy Solution

STEP 1

1. A reference angle is the smallest angle that the terminal side of a given angle makes with the x-axis.
2. Reference angles are always positive and less than or equal to $90^\circ$ .

STEP 2

1. Determine the quadrant in which the angle lies.
2. Calculate the reference angle.

STEP 3

First, determine the quadrant for the angle $192^\circ$ . Angles between $180^\circ$ and $270^\circ$ lie in the third quadrant.

STEP 4

In the third quadrant, the reference angle is found by subtracting $180^\circ$ from the given angle. This is because the reference angle is the angle between the terminal side and the negative x-axis.

STEP 5

Calculate the reference angle:
$192^\circ - 180^\circ = 12^\circ$
The reference angle for $192^\circ$ is:
$\boxed{12^\circ}$

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QuestionFind the reference angle for 192 degrees.

Studdy Solution

STEP 1

1. A reference angle is the smallest angle that the terminal side of a given angle makes with the x-axis.2. Reference angles are always positive and less than or equal to 90∘ 90^\circ 90∘.

STEP 2

1. Determine the quadrant in which the angle lies.2. Calculate the reference angle.

STEP 3

First, determine the quadrant for the angle 192∘ 192^\circ 192∘. Angles between 180∘ 180^\circ 180∘ and 270∘ 270^\circ 270∘ lie in the third quadrant.

STEP 4

In the third quadrant, the reference angle is found by subtracting 180∘ 180^\circ 180∘ from the given angle. This is because the reference angle is the angle between the terminal side and the negative x-axis.

STEP 5

Calculate the reference angle:192∘−180∘=12∘ 192^\circ - 180^\circ = 12^\circ 192∘−180∘=12∘ The reference angle for 192∘ 192^\circ 192∘ is:12∘ \boxed{12^\circ} 12∘​

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1. A reference angle is the smallest angle that the terminal side of a given angle makes with the x-axis.
2. Reference angles are always positive and less than or equal to $90^\circ$ .

1. Determine the quadrant in which the angle lies.
2. Calculate the reference angle.

First, determine the quadrant for the angle $192^\circ$ . Angles between $180^\circ$ and $270^\circ$ lie in the third quadrant.

In the third quadrant, the reference angle is found by subtracting $180^\circ$ from the given angle. This is because the reference angle is the angle between the terminal side and the negative x-axis.

Calculate the reference angle:
$192^\circ - 180^\circ = 12^\circ$
The reference angle for $192^\circ$ is:
$\boxed{12^\circ}$