Convert the angle measure to degrees to radians. -5pi/4 degrees is the same as what degrees?
The Correct Answer and Explanation is:
There seems to be a small mix-up in your question. You wrote:
“-5π/4 degrees”
But π (pi) typically indicates a radian measure, not degrees. So, we need to clarify:
- If you meant “-5π/4 radians”, then we can convert that to degrees.
- If you meant “-5π/4 degrees”, then it’s already in degrees, though it’s an unusual way to write degrees.
Assuming you meant “-5π/4 radians”, here’s the correct answer and explanation:
✅ Final Answer:
-5π/4 radians = -225 degrees
🧠 Explanation
In trigonometry, angles can be measured in degrees or radians. A full circle is 360 degrees or 2π radians. So the key conversion factor between the two units is: 180∘=π radians180^\circ = \pi \text{ radians}180∘=π radians
To convert from radians to degrees, use the formula: Degrees=Radians×180∘π\text{Degrees} = \text{Radians} \times \frac{180^\circ}{\pi}Degrees=Radians×π180∘
Let’s apply that to the angle -5π/4 radians: Degrees=(−5π4)×180∘π\text{Degrees} = \left(-\frac{5\pi}{4}\right) \times \frac{180^\circ}{\pi}Degrees=(−45π)×π180∘
Notice how the π terms cancel out: =−5⋅1804=−9004=−225∘= -\frac{5 \cdot 180}{4} = -\frac{900}{4} = -225^\circ=−45⋅180=−4900=−225∘
So, -5π/4 radians is equal to -225 degrees.
The negative sign tells us the angle is measured in the clockwise direction from the positive x-axis, which is typical for negative angle measures. If we visualize it on the unit circle, -225° rotates us 225 degrees clockwise, landing us in the third quadrant, the same position as 135° counterclockwise.
Summary:
- π radians = 180°
- Multiply radians by 180/π to convert to degrees
- -5π/4 × 180/π = -225°
Always keep track of whether you’re working in radians or degrees — many mistakes in trigonometry happen because of unit confusion.
