Question

Convert each angle in degrees to radians. Express your answer in decimal form, rounded to two decimal places. \(73^{\circ}\)

Short answer

1.27 radians

Step-by-step solution

Understand the conversion formula

To convert an angle from degrees to radians, use the formula: \[ \text{radians} = \text{degrees} \times \frac{\text{π}}{180} \]

Substitute the given angle

Substitute \( 73^{\text{°}} \) into the conversion formula: \[ 73 \times \frac{\text{π}}{180} \]

Compute the multiplication

First, multiply 73 by π: \[ 73 \times 3.14159 = 229.33657 \]

Divide by 180

Next, divide the result by 180 to convert to radians: \[ \frac{229.33657}{180} \ \text{= 1.27409} \]

Round to two decimal places

Finally, round the result to two decimal places: \[ 1.27 \]

Key concepts

Degrees to Radians

Angles in geometry can be measured in degrees or radians. Degrees are more common in everyday use, while radians are often used in higher mathematics, including trigonometry and calculus. The main idea when converting from degrees to radians is to use a standard conversion factor that relates the two.

Conversion Formula

The conversion formula for changing degrees to radians is simple to use. It is:

\( \text{radians} = \text{degrees} \times \frac{\text{π}}{180} \)

This formula works because there are \( 180^\text{°} \) in \( \text{π} \) radians. So to convert any angle from degrees to radians, you multiply the angle in degrees by \( \text{π}/180 \).

Rounding Decimals

When you convert an angle to radians, you might not get a whole number. In mathematics, it's often useful to round this number to a certain number of decimal places. In this exercise, we round to two decimal places. To do this:

• Identify the position of the second decimal place.
• Look at the digit in the third decimal place to see if it is 5 or greater.
• If it is 5 or greater, round the second decimal digit up by one.
• If it is less than 5, leave the second decimal digit as it is.

For example, if the value is 1.27409, rounding to two decimal places gives 1.27.

Trigonometry

Trigonometry is a branch of mathematics that studies the relationships between the angles and sides of triangles. Radians are particularly useful in trigonometry because many of the formulas used become simpler when angles are expressed in radians rather than degrees.

Understanding how to convert between degrees and radians is fundamental in trigonometry and helps in solving various trigonometric problems efficiently.