Question

convert 150 degree into radians​

Answer 1

Answer:2.6179

Explanation:

The amount of rotation to get the end side from the start side is called the measure of the angle. There are different units for measuring angles. The most commonly used angle measurement units are degrees and radians. The relationship between degree and radian measures of angles is used to convert a given angle measurement from one unit to another unit. Before we understand the relationship between the degree measure and the radian measure, let's recall the measure and the radian measure.

Degree measure

If the rotation from the start side to the end side is (1/360) of a revolution, then the angle is said to have a measure of one degree, written as 1°.

Radian measure

The angle subtended at the center by an arc of length 1 unit in a circular unit has a value of 1 radian.

The complete angle of a circle is 360 degrees 2π radians. This is the basis for converting angle measures from one unit to another. This means that a circle subtends an angle whose radian measure is 2π and whose degree measure is 360° at the center. This can be written as:

2π radian = 360°

or

π radian = 180°

The above relation allows us to formulate the measure in radians in degree measures and the measure in radians. By substituting this value into the above relationship, we get;

1 radian = 180°/π = 57° 16′ (approximate)

Also,

1° = π/180 radian = 0.01746 radian (approx)

Hence,

150°=150×0.01746=2.6179

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