Math / Trigonometry

QuestionTrigonometric Functions / The Unit Circle Given the standard position angle $\theta=555^{\circ}$ , state the measure of the reference angle. Your answer must be exact. Use Pi for $\pi$ .
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Studdy Solution

STEP 1

1. The angle $\theta$ is given in degrees.
2. A full rotation around a circle is $360^\circ$ .
3. The reference angle is the acute angle formed by the terminal side of $\theta$ and the horizontal axis.

STEP 2

1. Determine the equivalent angle within one full circle.
2. Calculate the reference angle.

STEP 3

First, we need to find the equivalent angle of $\theta = 555^\circ$ within one full circle. To do this, subtract $360^\circ$ from $555^\circ$ until the result is less than $360^\circ$ .

STEP 4

Calculate $555^\circ - 360^\circ = 195^\circ$ . The angle $195^\circ$ is the equivalent angle within one full circle.

STEP 5

Now, determine the reference angle. Since $195^\circ$ is in the third quadrant, the reference angle is calculated as $180^\circ - 195^\circ$ .

STEP 6

Calculate the reference angle: $195^\circ - 180^\circ = 15^\circ$ .
The measure of the reference angle for $\theta = 555^\circ$ is:
$\boxed{15^\circ}$

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QuestionTrigonometric Functions / The Unit Circle Given the standard position angle $\theta=555^{\circ}$ , state the measure of the reference angle. Your answer must be exact. Use Pi for $\pi$ .
How Did I Do? Try Another

Studdy Solution

STEP 1

1. The angle $\theta$ is given in degrees.
2. A full rotation around a circle is $360^\circ$ .
3. The reference angle is the acute angle formed by the terminal side of $\theta$ and the horizontal axis.

STEP 2

1. Determine the equivalent angle within one full circle.
2. Calculate the reference angle.

STEP 3

First, we need to find the equivalent angle of $\theta = 555^\circ$ within one full circle. To do this, subtract $360^\circ$ from $555^\circ$ until the result is less than $360^\circ$ .

STEP 4

Calculate $555^\circ - 360^\circ = 195^\circ$ . The angle $195^\circ$ is the equivalent angle within one full circle.

STEP 5

Now, determine the reference angle. Since $195^\circ$ is in the third quadrant, the reference angle is calculated as $180^\circ - 195^\circ$ .

STEP 6

Calculate the reference angle: $195^\circ - 180^\circ = 15^\circ$ .
The measure of the reference angle for $\theta = 555^\circ$ is:
$\boxed{15^\circ}$

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QuestionTrigonometric Functions / The Unit Circle Given the standard position angle θ=555∘\theta=555^{\circ}θ=555∘, state the measure of the reference angle. Your answer must be exact. Use Pi for π\piπ.How Did I Do? Try Another

Studdy Solution

STEP 1

1. The angle θ\thetaθ is given in degrees.2. A full rotation around a circle is 360∘360^\circ360∘.3. The reference angle is the acute angle formed by the terminal side of θ\thetaθ and the horizontal axis.

STEP 2

1. Determine the equivalent angle within one full circle.2. Calculate the reference angle.

STEP 3

First, we need to find the equivalent angle of θ=555∘\theta = 555^\circθ=555∘ within one full circle. To do this, subtract 360∘360^\circ360∘ from 555∘555^\circ555∘ until the result is less than 360∘360^\circ360∘.

STEP 4

Calculate 555∘−360∘=195∘555^\circ - 360^\circ = 195^\circ555∘−360∘=195∘. The angle 195∘195^\circ195∘ is the equivalent angle within one full circle.

STEP 5

Now, determine the reference angle. Since 195∘195^\circ195∘ is in the third quadrant, the reference angle is calculated as 180∘−195∘180^\circ - 195^\circ180∘−195∘.

STEP 6

Calculate the reference angle: 195∘−180∘=15∘195^\circ - 180^\circ = 15^\circ195∘−180∘=15∘. The measure of the reference angle for θ=555∘\theta = 555^\circθ=555∘ is:15∘ \boxed{15^\circ} 15∘​

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QuestionTrigonometric Functions / The Unit Circle Given the standard position angle $\theta=555^{\circ}$ , state the measure of the reference angle. Your answer must be exact. Use Pi for $\pi$ .
How Did I Do? Try Another

1. The angle $\theta$ is given in degrees.
2. A full rotation around a circle is $360^\circ$ .
3. The reference angle is the acute angle formed by the terminal side of $\theta$ and the horizontal axis.

1. Determine the equivalent angle within one full circle.
2. Calculate the reference angle.

First, we need to find the equivalent angle of $\theta = 555^\circ$ within one full circle. To do this, subtract $360^\circ$ from $555^\circ$ until the result is less than $360^\circ$ .

Calculate $555^\circ - 360^\circ = 195^\circ$ . The angle $195^\circ$ is the equivalent angle within one full circle.

Now, determine the reference angle. Since $195^\circ$ is in the third quadrant, the reference angle is calculated as $180^\circ - 195^\circ$ .

Calculate the reference angle: $195^\circ - 180^\circ = 15^\circ$ .
The measure of the reference angle for $\theta = 555^\circ$ is:
$\boxed{15^\circ}$