Convert 225° to radians.

Question

Accepted Answer

5π/4. The correct answer is 5π/4. To convert degrees to radians, multiply by π/180: 225° × (π/180) = 225π/180 = 5π/4. This angle lies in the third quadrant (between π and 3π/2), where both sine and cosine are negative.

The value 3π/4 equals 135°, which is in the second quadrant, not the third. The value 7π/4 equals 315°, which is in the fourth quadrant. The value 5π/6 equals 150°, which is also in the second quadrant. Each of these represents a different angle that does not equal 225°.

Degree-radian conversion is a fundamental skill for the CLEP Precalculus exam. Students should memorize key equivalences: 30° = π/6, 45° = π/4, 60° = π/3, 90° = π/2, 180° = π, 270° = 3π/2, 360° = 2π. For angles like 225°, recognizing it as 180° + 45° helps: π + π/4 = 5π/4. Being fluent with both units is essential for all trigonometric work.

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