Unit of plane angle is ____________.

A. Radian

B. Steradian

C. Degree

D. Celsius

The unit of plane angle is primarily measured in radians. So, the correct answer to your question is A. Radian. Let’s delve deeper into what this means and why radians are the standard unit for measuring angles in many mathematical and scientific contexts.

Understanding Plane Angles

A plane angle is formed when two rays (or lines) originate from a common point, known as the vertex. The amount of rotation from one ray to the other defines the angle. To quantify this rotation, we use various units, with radians and degrees being the most common.

Radians Explained

A radian is defined based on the radius of a circle. Specifically, one radian is the angle created when the arc length of a circle is equal to the radius of that circle. This relationship gives rise to a natural way of measuring angles that is particularly useful in calculus and physics.

Degrees as an Alternative

Degrees are another way to measure angles, where a full circle is divided into 360 parts. While degrees are widely used in everyday contexts, such as in navigation and geometry, radians are often preferred in advanced mathematics because they simplify many formulas, especially those involving trigonometric functions.

Why Radians Are Important

Using radians can make calculations more straightforward. For example, the derivative of the sine function is the cosine function when angles are measured in radians, which is not the case when using degrees. This property is crucial in calculus and helps in solving problems involving periodic functions.

Other Units of Measurement

While radians and degrees are the most common units for measuring angles, you might also encounter steradians, which measure solid angles in three-dimensional space. However, steradians are not applicable when discussing plane angles, which is why they are not the correct answer in this context.

Practical Examples

• If you have a circle with a radius of 1 meter, an angle of 1 radian corresponds to an arc length of 1 meter on the circumference of that circle.
• In practical applications, engineers often use radians when designing systems involving rotational motion, as it leads to more efficient calculations.

In summary, while degrees are familiar and useful in many situations, radians provide a more natural and mathematically elegant way to measure angles, especially in higher-level mathematics and physics. Thus, the unit of plane angle is indeed the radian.