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.

9. Unit Circle

Reference Angles

Precalculus

9. Unit Circle

Reference Angles

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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 the concept of a reference angle. A 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 π/2 radians.

Step 2: For the angle $ \frac{7\pi}{4} $, determine its position on the unit circle. Since $ \frac{7\pi}{4} $ is greater than $ \pi $, it is in the fourth quadrant. To find the reference angle, subtract $ \frac{7\pi}{4} $ from $ 2\pi $.

Step 3: For the angle $ \frac{\pi}{6} $, determine its position on the unit circle. Since $ \frac{\pi}{6} $ is less than $ \pi $, it is in the first quadrant. The reference angle is the angle itself, $ \frac{\pi}{6} $.

Step 4: For the angle $ \frac{\pi}{3} $, determine its position on the unit circle. Since $ \frac{\pi}{3} $ is less than $ \pi $, it is in the first quadrant. The reference angle is the angle itself, $ \frac{\pi}{3} $.

Step 5: Compare the reference angles found: $ \frac{\pi}{4} $ is the reference angle for $ \frac{7\pi}{4} $, $ \frac{\pi}{6} $ for $ \frac{\pi}{6} $, and $ \frac{\pi}{3} $ for $ \frac{\pi}{3} $. The correct answer is $ \frac{\pi}{4} $ as the reference angle for $ \frac{7\pi}{4} $.

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

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