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 seven pi over four. 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 four up here in quadrant one pi over four, 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 four radians or 45 degrees away from that nearest point on the x axis so that tells me that the reference angle of seven pi over four is pi over four radians or 45 degrees. Thanks for watching and let me know if you have questions.

12. Trigonometric Functions

Trigonometric Functions on the Unit Circle

Business Calculus

12. Trigonometric Functions

Trigonometric Functions on the Unit Circle

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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 acute angle formed by the terminal side of a given angle and the x-axis. It is always positive and lies between 0 and π/2 radians.

Step 2: For each given angle, determine its position on the unit circle. Identify the quadrant in which the terminal side of the angle lies. For example, 7π/4 lies in the fourth quadrant, π/6 lies in the first quadrant, and π/3 lies in the first quadrant.

Step 3: Use the formula for reference angles based on the quadrant. In the first quadrant, the reference angle is the angle itself. In the second quadrant, subtract the angle from π. In the third quadrant, subtract π from the angle. In the fourth quadrant, subtract the angle from 2π.

Step 4: Apply the formula to each angle. For 7π/4, subtract it from 2π to find the reference angle. For π/6 and π/3, since they are in the first quadrant, their reference angles are the angles themselves.

Step 5: Verify that the reference angles are acute (between 0 and π/2 radians) and positive. The reference angles for the given angles are π/4 for 7π/4, π/6 for π/6, and π/3 for π/3.