Convert the angle measure from radians to degrees. -5pi/12 is the same as what
To convert −5π12-\frac{5\pi}{12}−125π radians to degrees, use the conversion factor:1 radian=180∘π1 \text{ radian} = \frac{180^\circ}{\pi}1 radian=π180∘
Step-by-step Conversion:
−5π12 radians=−5π12×180∘π-\frac{5\pi}{12} \text{ radians} = -\frac{5\pi}{12} \times \frac{180^\circ}{\pi}−125π radians=−125π×π180∘
Cancel out π\piπ:=−5×180∘12= -\frac{5 \times 180^\circ}{12}=−125×180∘=−900∘12= -\frac{900^\circ}{12}=−12900∘=−75∘= -75^\circ=−75∘
Final Answer:
−5π12 radians=−75∘-\frac{5\pi}{12} \text{ radians} = -75^\circ−125π radians=−75∘
Explanation:
Angles can be measured in radians or degrees, which are two different units for the same concept. Radians are often used in mathematics and physics, especially when dealing with trigonometric functions and calculus. Degrees, on the other hand, are more commonly used in geometry and everyday applications.
To convert an angle from radians to degrees, we use the fact that a full circle is 2π2\pi2π radians or 360∘360^\circ360∘. From this relationship, we derive the conversion factor:1 radian=180∘π1 \text{ radian} = \frac{180^\circ}{\pi}1 radian=π180∘
This tells us that to convert any radian measure to degrees, we multiply it by 180∘π\frac{180^\circ}{\pi}π180∘.
In the case of −5π12-\frac{5\pi}{12}−125π, we start by multiplying it by 180∘π\frac{180^\circ}{\pi}π180∘. The π\piπ terms cancel out, and we are left with:−5×18012-\frac{5 \times 180}{12}−125×180
We then calculate the numerator: 5×180=9005 \times 180 = 9005×180=900, and divide by 12, which gives us 75. Because the original angle was negative, the final answer is −75∘-75^\circ−75∘.
A negative angle means the rotation is clockwise, as opposed to a positive angle, which represents a counterclockwise rotation. So, −5π12-\frac{5\pi}{12}−125π radians is a clockwise rotation of 75 degrees from the positive x-axis.
Understanding this conversion is fundamental in trigonometry, engineering, physics, and computer graphics where angle measures often need to be translated between the two units depending on the context.
