Convert 150∘ to Radian

The Correct Answer and Explanation is:

ChatGPT said:

To convert 150° to radians, we use the standard conversion formula:Radians=Degrees×(π180)\text{Radians} = \text{Degrees} \times \left( \frac{\pi}{180} \right)Radians=Degrees×(180π​)

Applying this to 150°:150∘×(π180)=150π180=5π6150^\circ \times \left( \frac{\pi}{180} \right) = \frac{150\pi}{180} = \frac{5\pi}{6}150∘×(180π​)=180150π​=65π​

✅ Final Answer:

150∘=5π6 radians150^\circ = \frac{5\pi}{6} \text{ radians}150∘=65π​ radians

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📘 Explanation

In mathematics, angles can be measured in degrees or radians. Degrees are more familiar in everyday contexts (like 90° for a right angle), but radians are used more often in higher-level math, especially in calculus and trigonometry, because they simplify many formulas.

The radian is based on the radius of a circle. One full circle (360°) is equal to 2π radians. This relationship leads to the conversion factor:1∘=π180 radians1^\circ = \frac{\pi}{180} \text{ radians}1∘=180π​ radians

To convert any angle from degrees to radians, multiply by π180\frac{\pi}{180}180π​. For 150°, we compute:150×π180=150π180150 \times \frac{\pi}{180} = \frac{150\pi}{180}150×180π​=180150π​

Next, simplify the fraction:150π180=5π6\frac{150\pi}{180} = \frac{5\pi}{6}180150π​=65π​

This means that an angle of 150° corresponds to 5π6\frac{5\pi}{6}65π​ radians.

This is important in many applications, such as finding the sine or cosine of an angle, solving trigonometric equations, or analyzing circular motion. Radians are especially useful in calculus because the derivatives of trigonometric functions like sin(x) and cos(x) are only accurate in radians.

Understanding this conversion helps students move between the familiar world of degrees and the mathematically convenient world of radians, enhancing problem-solving flexibility in geometry, physics, and engineering.