Math / Trigonometry

QuestionFind the measure of a positive angle coterminal with $-540^{\circ}$ . $\square$

Studdy Solution

STEP 1

1. Coterminal angles differ by full rotations of $360^\circ$ .
2. We need to find a positive angle coterminal with $-540^\circ$ .

STEP 2

1. Determine the equivalent positive angle.
2. Adjust the angle to be within the standard $0^\circ$ to $360^\circ$ range.

STEP 3

To find a coterminal angle, we add or subtract $360^\circ$ until the angle is positive. Start with the given angle:
$-540^\circ$

STEP 4

Add $360^\circ$ to $-540^\circ$ to find a coterminal angle:
$-540^\circ + 360^\circ = -180^\circ$

STEP 5

The result is still negative, so add $360^\circ$ again:
$-180^\circ + 360^\circ = 180^\circ$

STEP 6

Verify that the angle $180^\circ$ is within the standard range of $0^\circ$ to $360^\circ$ . Since it is, this is the positive coterminal angle.
The measure of a positive angle coterminal with $-540^\circ$ is:
$\boxed{180^\circ}$

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QuestionFind the measure of a positive angle coterminal with $-540^{\circ}$ . $\square$

Studdy Solution

STEP 1

1. Coterminal angles differ by full rotations of $360^\circ$ .
2. We need to find a positive angle coterminal with $-540^\circ$ .

STEP 2

1. Determine the equivalent positive angle.
2. Adjust the angle to be within the standard $0^\circ$ to $360^\circ$ range.

STEP 3

To find a coterminal angle, we add or subtract $360^\circ$ until the angle is positive. Start with the given angle:
$-540^\circ$

STEP 4

Add $360^\circ$ to $-540^\circ$ to find a coterminal angle:
$-540^\circ + 360^\circ = -180^\circ$

STEP 5

The result is still negative, so add $360^\circ$ again:
$-180^\circ + 360^\circ = 180^\circ$

STEP 6

Verify that the angle $180^\circ$ is within the standard range of $0^\circ$ to $360^\circ$ . Since it is, this is the positive coterminal angle.
The measure of a positive angle coterminal with $-540^\circ$ is:
$\boxed{180^\circ}$

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QuestionFind the measure of a positive angle coterminal with −540∘-540^{\circ}−540∘. □\square□

Studdy Solution

STEP 1

1. Coterminal angles differ by full rotations of 360∘ 360^\circ 360∘.2. We need to find a positive angle coterminal with −540∘ -540^\circ −540∘.

STEP 2

1. Determine the equivalent positive angle.2. Adjust the angle to be within the standard 0∘ 0^\circ 0∘ to 360∘ 360^\circ 360∘ range.

STEP 3

To find a coterminal angle, we add or subtract 360∘ 360^\circ 360∘ until the angle is positive. Start with the given angle:−540∘ -540^\circ −540∘

STEP 4

Add 360∘ 360^\circ 360∘ to −540∘ -540^\circ −540∘ to find a coterminal angle:−540∘+360∘=−180∘ -540^\circ + 360^\circ = -180^\circ −540∘+360∘=−180∘

STEP 5

The result is still negative, so add 360∘ 360^\circ 360∘ again:−180∘+360∘=180∘ -180^\circ + 360^\circ = 180^\circ −180∘+360∘=180∘

STEP 6

Verify that the angle 180∘ 180^\circ 180∘ is within the standard range of 0∘ 0^\circ 0∘ to 360∘ 360^\circ 360∘. Since it is, this is the positive coterminal angle. The measure of a positive angle coterminal with −540∘ -540^\circ −540∘ is:180∘ \boxed{180^\circ} 180∘​

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QuestionFind the measure of a positive angle coterminal with $-540^{\circ}$ . $\square$

1. Coterminal angles differ by full rotations of $360^\circ$ .
2. We need to find a positive angle coterminal with $-540^\circ$ .

1. Determine the equivalent positive angle.
2. Adjust the angle to be within the standard $0^\circ$ to $360^\circ$ range.

To find a coterminal angle, we add or subtract $360^\circ$ until the angle is positive. Start with the given angle:
$-540^\circ$

Add $360^\circ$ to $-540^\circ$ to find a coterminal angle:
$-540^\circ + 360^\circ = -180^\circ$

The result is still negative, so add $360^\circ$ again:
$-180^\circ + 360^\circ = 180^\circ$

Verify that the angle $180^\circ$ is within the standard range of $0^\circ$ to $360^\circ$ . Since it is, this is the positive coterminal angle.
The measure of a positive angle coterminal with $-540^\circ$ is:
$\boxed{180^\circ}$