Identify the reference angle of each given angle. 7 π 4 \frac{7\pi}{4} 4 7 π rad

In this problem, we're asked to identify the reference angle of the given angle, and the angle that we're given here is 7 pi over 4. Now you could choose just to kind of memorize what the reference angle is here by looking at that denominator because I know that the denominator of its reference angle is the exact same 4 up here in quadrant 1, pi over 4. But you can also think about this by actually going to take a look at your angle on the unit circle and measuring it here from the nearest point of the x axis. Now from that nearest point of the x axis, I know that it is pi over 4 radians or 45 degrees away from that nearest point on the x axis. So that tells me that the reference angle of 7 pi over 4 is pi over 4 radians or 45 degrees. Thanks for watching and let me know if you have questions.

3. Unit Circle

Reference Angles

Trigonometry

3. Unit Circle

Reference Angles

Struggling with Trigonometry?

Join thousands of students who trust us to help them ace their exams!

Multiple Choice

Identify the reference angle of each given angle.
$\frac{7\pi}{4}$ rad

$\frac{\pi}{6}$

$\frac{\pi}{4}$

$\frac{\pi}{3}$

Verified step by step guidance

Step 1: Understand that the reference angle is the smallest angle that the terminal side of a given angle makes with the x-axis. It is always positive and less than or equal to $ \frac{\pi}{2} $ radians.

Step 2: For the angle $ \frac{7\pi}{4} $, first determine its position in the unit circle. Since $ \frac{7\pi}{4} $ is greater than $ 2\pi $, subtract $ 2\pi $ to find its equivalent angle within the first full rotation: $ \frac{7\pi}{4} - 2\pi = \frac{7\pi}{4} - \frac{8\pi}{4} = -\frac{\pi}{4} $. The reference angle is $ \frac{\pi}{4} $.

Step 3: For the angle $ \frac{\pi}{6} $, since it is already between 0 and $ \frac{\pi}{2} $, it is its own reference angle. Therefore, the reference angle is $ \frac{\pi}{6} $.

Step 4: For the angle $ \frac{\pi}{3} $, similarly, since it is also between 0 and $ \frac{\pi}{2} $, it is its own reference angle. Therefore, the reference angle is $ \frac{\pi}{3} $.

Step 5: Summarize the reference angles: $ \frac{7\pi}{4} $ has a reference angle of $ \frac{\pi}{4} $, $ \frac{\pi}{6} $ has a reference angle of $ \frac{\pi}{6} $, and $ \frac{\pi}{3} $ has a reference angle of $ \frac{\pi}{3} $.

5:31m

Watch next

Master Reference Angles on the Unit Circle with a bite sized video explanation from Patrick

Reference Angles practice set

Problem sets built by lead tutors

Expert video explanations

Struggling with Trigonometry?

Identify the reference angle of each given angle.7π4\(\frac{7\pi}{4}\)47π rad

Watch next

Reference Angles practice set

Identify the reference angle of each given angle.
$\frac{7\pi}{4}$ rad