Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Question
Find an angle in each quadrant with a common reference angle with
165^(@), from
0^(@) <= theta < 360^(@)
Answer Attempt 1 out of 2
Quadrant I: Quadrant II:
Quadrant III:
Quadrant IV:
Submit Answer

Question $\newline$ Find an angle in each quadrant with a common reference angle with $165^{\circ}$ , from $0^{\circ} \leq \theta<360^{\circ}$ $\newline$ Answer Attempt $1$ out of $2$ $\newline$ Quadrant I: Quadrant II: $\newline$ Quadrant III: $\newline$ Quadrant IV: $\newline$ Submit Answer

View step-by-step help

View step-by-step help

Full solution

Q. Question

\newline

Find an angle in each quadrant with a common reference angle with

165^{\circ}

, from

0^{\circ} \leq \theta<360^{\circ}

\newline

Answer Attempt

1

out of

2

\newline

Quadrant I: Quadrant II:

\newline

Quadrant III:

\newline

Quadrant IV:

\newline

Submit Answer

Find Reference Angle: The reference angle is the acute angle that an angle makes with the x-axis. To find the reference angle for $165$ degrees, which is in Quadrant II, we subtract it from $180$ degrees because it's the closest x-axis angle for angles in Quadrant II. $\newline$ Reference angle = $180$ degrees - $165$ degrees = $15$ degrees.
Quadrant I Angle: For Quadrant I, the angle with the same reference angle would be its own measure since reference angles in Quadrant I are the angles themselves. Therefore, the angle in Quadrant I is $15$ degrees.
Quadrant II Angle: For Quadrant II, the angle is $165$ degrees, which is given in the problem.
Quadrant III Angle: For Quadrant III, we add $180$ degrees to the reference angle because angles in Quadrant III are $180$ degrees plus their reference angle. $\newline$ Quadrant III angle = $180$ degrees + $15$ degrees = $195$ degrees.
Quadrant IV Angle: For Quadrant IV, we subtract the reference angle from $360$ degrees because angles in Quadrant IV are $360$ degrees minus their reference angle. $\newline$ Quadrant IV angle = $360$ degrees $-$ $15$ degrees = $345$ degrees.

More problems from Quadrants

Question

Find the measure of a negative angle coterminal with

180^\circ

\newline

^\circ

Posted 2 months ago

Question

Find the measure of the reference angle for a

170^\circ

Posted 1 month ago

Question

How many radians is

60^\circ

\newline

\newline

[A]\frac{\pi}{3}\text{ radians}

\newline

[B]\frac{\pi}{2}\text{ radians}

\newline

[C]\frac{\pi}{4}\text{ radians}

\newline

[D]\frac{\pi}{6}\text{ radians}

Posted 2 months ago

Question

Which of the following radian measures is equal to

90^{\circ}

\newline

1

\newline

\frac{\pi}{3}

\newline

\frac{\pi}{4}

\newline

\frac{\pi}{2}

\newline

\frac{\pi}{6}

Posted 2 months ago

Question

Which of the following radian measures is equal to

225^{\circ}

\newline

1

\newline

\frac{\pi}{4}

\newline

\frac{\pi}{2}

\newline

\frac{3 \pi}{4}

\newline

\frac{5 \pi}{4}

Posted 4 months ago

Question

Which of the following radian measures is equal to

135^{\circ}

\newline

1

\newline

\frac{\pi}{4}

\newline

\frac{\pi}{2}

\newline

\frac{3 \pi}{4}

\newline

\pi

Posted 4 months ago

Question

Which of the following radian measures is equal to

330^{\circ}

\newline

1

\newline

\frac{15 \pi}{6}

\newline

\frac{7 \pi}{6}

\newline

\frac{11 \pi}{6}

\newline

\frac{13 \pi}{6}

Posted 4 months ago

Question

Which of the following radian measures is equal to

75^{\circ}

\newline

1

\newline

\frac{\pi}{12}

\newline

\frac{\pi}{3}

\newline

\frac{5 \pi}{12}

\newline

\frac{7 \pi}{12}

Posted 2 months ago

Question

Which of the following radian measures is equal to

240^{\circ}

\newline

1

\newline

\frac{4 \pi}{3}

\newline

\frac{5 \pi}{3}

\newline

\frac{7 \pi}{3}

\newline

\frac{11 \pi}{3}

Posted 4 months ago

Question

Which of the following radian measures is equal to

120^{\circ}

\newline

1

\newline

\frac{2 \pi}{3}

\newline

\pi

\newline

\frac{4 \pi}{3}

\newline

\frac{5 \pi}{3}

Posted 4 months ago