Question

Convert each angle in degrees to radians. Express your answer in decimal form, rounded to two decimal places. \(-51^{\circ}\)

Short answer

-0.89 radians.

Step-by-step solution

- Understand the Conversion Formula

To convert an angle from degrees to radians, use the formula: \[\text{radians} = \text{degrees} \times \frac{\text{π}}{180}\] where π (pi) is approximately 3.14159.

- Substitute the Given Angle

Substitute \text{-51^{\text{°}}}\ into the conversion formula: \[\text{radians} = -51 \times \frac{\text{π}}{180}\]

- Perform the Multiplication

Calculate the multiplication: \[-51 \times \frac{3.14159}{180} \ = -0.89012\]

- Round the Result

Round the result to two decimal places: \[-0.89012 \ \text{is approximately} \ -0.89\]

Key concepts

degree to radian conversion

Converting degrees to radians is an essential task in trigonometry and requires understanding a simple formula. Basically, this conversion is about switching from one way of measuring angles to another.
Degrees and radians are both units for measuring angles, but they are used in different contexts. The formula to convert degrees to radians is given by: \[\text{radians} = \text{degrees} \times \frac{\text{π}}{180}\] Here, π (pi) is a constant approximately equal to 3.14159.
To illustrate this, let's look at the example of converting \(-51^{\text{°}}\) to radians.
1. Substitute \(-51^{\text{°}}\) into the formula: \[\text{radians} = -51 \times \frac{\text{π}}{180}\] 2. Calculate the multiplication: \[-51 \times \frac{3.14159}{180} = -0.89012\] 3. Round the result: \-0.89012 rounded to two decimal places is \-0.89

angle measurement

Angles are an important concept in mathematics and are measured in two primary units: degrees and radians. Understanding how these units work is crucial for solving many geometric and trigonometric problems.

• Degrees: This is the more common unit in everyday use, and a full circle is 360 degrees. A right angle, for example, is 90 degrees.
• Radians: This is often used in higher mathematics and engineering. A full circle is 2π radians, which is approximately 6.28318 radians. Therefore, 180 degrees is equal to π radians.

Consider the example of converting \(-51^{\text{°}}\) to radians. This involves understanding that \-51^{\text{°}} is a measure of the angle, indicating the direction and size of rotation. Using the conversion relationship between degrees and radians helps in expressing this angle in another form, useful in various mathematical applications.

radian calculation

When calculating radians from degrees, you are effectively scaling the angle by the factor π/180. This process transforms the degree measure into its radian equivalent. This scaling factor is derived from the fact that 180 degrees equals π radians.
Let's break this down using our example:
1. Identify the angle in degrees: \-51^{\text{°}}. 2. Use the formula: multiplying the degree measure by the conversion factor \(\frac{\text{π}}{180}\). 3. Calculate: \-51 \times \frac{3.14159}{180} = -0.89012.
The result \-0.89012 is accurately our angle in radians.
Radians can be a more natural measure in many mathematical contexts, especially involving various mathematical functions and calculus. That’s why it is crucial to be comfortable with converting and calculating angles in radians.