In mathematics, angles are measured in various units, with degrees and radians being the most commonly used. The SAT Math section may include questions that require you to convert between these two angular measurement units. In this article, we will focus on a fundamental question: "How to convert 36° into radians?" We will explore the concept of radians, explain the conversion process, and provide a step-by-step solution to help you understand the procedure.

*Understanding Radians:*
Radians are a unit of angular measurement used primarily in trigonometry and calculus. Unlike degrees, which divide a circle into 360 equal parts, radians divide a circle into 2π (approximately 6.28319) equal parts. This unit is particularly useful in calculus because many trigonometric functions have simpler representations when angles are measured in radians.

*Conversion Formula:*
To convert degrees to radians, you can use the following formula:
Radians (rad) = Degrees (°) × (π / 180)
In this formula, π (pi) represents the mathematical constant approximately equal to 3.14159, and 180 is the number of degrees in a half-circle or π radians.

*Converting 36° to Radians:*

Now, let's apply the conversion formula to convert 36° into radians:
Radians (rad) = 36° × (π / 180)
Radians (rad) = 36 × (π / 180)
Radians (rad) = (36/180) × π

*Simplify the fraction:*
Radians (rad) = (1/5) × π

*Result:*
36° is equivalent to (1/5)π radians.

*Explanation:*

We start by using the conversion formula, multiplying 36° by (π / 180) to convert degrees to radians. We simplify the expression by dividing both the numerator and denominator by their greatest common factor, which is 36. The result, (1/5)π radians, represents the equivalent angle measurement in radians.

Converting degrees to radians is a fundamental mathematical skill that may be required in various contexts, including trigonometry and calculus. In this article, we discussed the concept of radians, provided the conversion formula, and demonstrated how to convert 36° into radians using step-by-step calculations. Understanding these principles will help you tackle similar questions on the SAT Math section with confidence and precision.

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