Math / Trigonometry

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For the rotation $-297^{\circ}$ , find the coterminal angle from $0^{\circ} \leq \theta<360^{\circ}$ , the quadrant, and the reference angle.
Answer Attempt 1 out of 2
The coterminal angle is of $\square$ ${ }^{\circ}$ 。 $\square$ ${ }^{\circ}$ , which lies in Quadrant Submit Answer

Studdy Solution

STEP 1

What is this asking? We need to find an angle between $0^\circ$ and $360^\circ$ that's essentially the same rotation as $-297^\circ$ , figure out which quadrant it's in, and find the smallest angle it makes with the x-axis. Watch out! Negative angles rotate clockwise, and we need a positive coterminal angle!
Also, the reference angle is always positive and less than or equal to $90^\circ$ .

STEP 2

1. Find the Coterminal Angle
2. Determine the Quadrant
3. Calculate the Reference Angle

STEP 3

Alright, so we're given this angle of $-297^\circ$ .
Since it's negative, it means we're rotating clockwise from the positive x-axis.
We want to find an angle between $0^\circ$ and $360^\circ$ that represents the same rotation, but going counter-clockwise!

STEP 4

To do this, we can add full rotations to our original angle until we land in the desired range.
A full rotation is $360^\circ$ , so let's add $360^\circ$ to $-297^\circ$ :
$-297^\circ + 360^\circ$

STEP 5

This gives us:
$-297^\circ + 360^\circ = 63^\circ$ Since $63^\circ$ is between $0^\circ$ and $360^\circ$ , this is our coterminal angle!

STEP 6

Now, let's see where this $63^\circ$ angle hangs out.
Remember: * Quadrant I: $0^\circ$ to $90^\circ$ * Quadrant II: $90^\circ$ to $180^\circ$ * Quadrant III: $180^\circ$ to $270^\circ$ * Quadrant IV: $270^\circ$ to $360^\circ$

STEP 7

Since $63^\circ$ is between $0^\circ$ and $90^\circ$ , our coterminal angle is chilling in Quadrant I!

STEP 8

The reference angle is the smallest angle our coterminal angle makes with the x-axis.
Since we're in Quadrant I, the reference angle is simply the coterminal angle itself!

STEP 9

Therefore, the reference angle is $63^\circ$ .

STEP 10

The coterminal angle is $63^\circ$ , which lies in Quadrant I.
The reference angle is $63^\circ$ .

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Studdy Solution

STEP 1

STEP 2

1. Find the Coterminal Angle
2. Determine the Quadrant
3. Calculate the Reference Angle

STEP 3

Alright, so we're given this angle of $-297^\circ$ .
Since it's negative, it means we're rotating clockwise from the positive x-axis.
We want to find an angle between $0^\circ$ and $360^\circ$ that represents the same rotation, but going counter-clockwise!

STEP 4

To do this, we can add full rotations to our original angle until we land in the desired range.
A full rotation is $360^\circ$ , so let's add $360^\circ$ to $-297^\circ$ :
$-297^\circ + 360^\circ$

STEP 5

This gives us:
$-297^\circ + 360^\circ = 63^\circ$ Since $63^\circ$ is between $0^\circ$ and $360^\circ$ , this is our coterminal angle!

STEP 6

Now, let's see where this $63^\circ$ angle hangs out.
Remember: * Quadrant I: $0^\circ$ to $90^\circ$ * Quadrant II: $90^\circ$ to $180^\circ$ * Quadrant III: $180^\circ$ to $270^\circ$ * Quadrant IV: $270^\circ$ to $360^\circ$

STEP 7

Since $63^\circ$ is between $0^\circ$ and $90^\circ$ , our coterminal angle is chilling in Quadrant I!

STEP 8

The reference angle is the smallest angle our coterminal angle makes with the x-axis.
Since we're in Quadrant I, the reference angle is simply the coterminal angle itself!

STEP 9

Therefore, the reference angle is $63^\circ$ .

STEP 10

The coterminal angle is $63^\circ$ , which lies in Quadrant I.
The reference angle is $63^\circ$ .

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Studdy Solution

STEP 1

STEP 2

1. Find the Coterminal Angle2. Determine the Quadrant3. Calculate the Reference Angle

STEP 3

Alright, so we're given this angle of −297∘-297^\circ−297∘.Since it's negative, it means we're rotating **clockwise** from the positive x-axis.We want to find an angle between 0∘0^\circ0∘ and 360∘360^\circ360∘ that represents the same rotation, but going **counter-clockwise**!

STEP 4

To do this, we can add **full rotations** to our original angle until we land in the desired range.A full rotation is 360∘360^\circ360∘, so let's add 360∘360^\circ360∘ to −297∘-297^\circ−297∘:−297∘+360∘-297^\circ + 360^\circ−297∘+360∘

STEP 5

This gives us:−297∘+360∘=63∘-297^\circ + 360^\circ = 63^\circ−297∘+360∘=63∘Since 63∘63^\circ63∘ is between 0∘0^\circ0∘ and 360∘360^\circ360∘, this is our **coterminal angle**!

STEP 6

STEP 7

Since 63∘63^\circ63∘ is between 0∘0^\circ0∘ and 90∘90^\circ90∘, our coterminal angle is chilling in **Quadrant I**!

STEP 8

The **reference angle** is the smallest angle our coterminal angle makes with the x-axis.Since we're in Quadrant I, the reference angle is simply the coterminal angle itself!

STEP 9

Therefore, the reference angle is 63∘63^\circ63∘.

STEP 10

The coterminal angle is 63∘63^\circ63∘, which lies in Quadrant I.The reference angle is 63∘63^\circ63∘.

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1. Find the Coterminal Angle
2. Determine the Quadrant
3. Calculate the Reference Angle

Alright, so we're given this angle of $-297^\circ$ .
Since it's negative, it means we're rotating clockwise from the positive x-axis.
We want to find an angle between $0^\circ$ and $360^\circ$ that represents the same rotation, but going counter-clockwise!

To do this, we can add full rotations to our original angle until we land in the desired range.
A full rotation is $360^\circ$ , so let's add $360^\circ$ to $-297^\circ$ :
$-297^\circ + 360^\circ$

This gives us:
$-297^\circ + 360^\circ = 63^\circ$ Since $63^\circ$ is between $0^\circ$ and $360^\circ$ , this is our coterminal angle!

Since $63^\circ$ is between $0^\circ$ and $90^\circ$ , our coterminal angle is chilling in Quadrant I!

The reference angle is the smallest angle our coterminal angle makes with the x-axis.
Since we're in Quadrant I, the reference angle is simply the coterminal angle itself!

Therefore, the reference angle is $63^\circ$ .

The coterminal angle is $63^\circ$ , which lies in Quadrant I.
The reference angle is $63^\circ$ .