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Math  /  Trigonometry

QuestionWhat angle (in radians) corresponds to 0.25 rotations around the unit circle? □\square radians (Give an exact answer as a fraction, not a decimal approximation.) help (angles)

Studdy Solution

STEP 1

1. One complete rotation around the unit circle is 2π 2\pi radians.
2. We need to find the angle in radians for 0.25 0.25 rotations.

STEP 2

1. Understand the relationship between rotations and radians.
2. Calculate the angle in radians for the given fraction of a rotation.

STEP 3

Recall that one complete rotation around the unit circle corresponds to 2π 2\pi radians. This is the fundamental relationship between rotations and radians.

STEP 4

To find the angle in radians for 0.25 0.25 rotations, we multiply the total radians for one full rotation by the fraction of the rotation. Thus, we have:
0.25×2π 0.25 \times 2\pi

STEP 5

Perform the multiplication:
0.25×2π=14×2π=2π4 0.25 \times 2\pi = \frac{1}{4} \times 2\pi = \frac{2\pi}{4}

STEP 6

Simplify the fraction:
2π4=π2 \frac{2\pi}{4} = \frac{\pi}{2}
The angle in radians that corresponds to 0.25 0.25 rotations around the unit circle is:
π2 \boxed{\frac{\pi}{2}}

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