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Chapter 4: Problem 10

Convert the given angle to degrees. \(35 \mathrm{rad}\)

Short Answer

Expert verified
2005.6 degrees

Step by step solution

01

- Understand the Conversion Factor

To convert radians to degrees, use the conversion factor that relates radians to degrees: 1 radian = \(\frac{180}{\pi}\) degrees.
02

- Set Up the Conversion

Multiply the given angle in radians by the conversion factor: \( 35 \text{ rad} \times \frac{180}{\pi} \text{ degrees} \).
03

- Perform the Calculation

Calculate the product: \( 35 \times \frac{180}{3.14159} = 35 \times 57.2958 = 2005.6 \text{ degrees} \).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Angle Conversion
Understanding angle conversion is essential in trigonometry and various practical applications.
Angles can be measured in degrees or radians, but sometimes you need to convert from one unit to another.
This is where angle conversion comes into play.
To convert between degrees and radians, use specific formulas.
Degrees measure angles based on dividing a circle into 360 equal parts, where a full circle equals 360 degrees.
Radians measure angles based on the radius of a circle.
One full circle is \( \text{2蟺} \) radians.
Radian to Degree Conversion
Converting radians to degrees involves a specific conversion factor.
Here's a simplified process:
  • 1 radian is equal to \( \frac{180}{\text{蟺}} \) degrees.
  • To convert radians to degrees, multiply the angle in radians by \( \frac{180}{\text{蟺}} \).

Let's apply this to convert 35 radians to degrees:
Use the formula:
\( 35 \text{ rad} \times \frac{180}{\text{蟺}} \)
Replace \( \text{蟺} \) with its approximate value 3.14159:
\( 35 \text{ rad} \times \frac{180}{3.14159} \)
This equals approximately:
\( 35 \text{ rad} \times 57.2958 \)
Resulting in around 2005.6 degrees.
Trigonometry Basics
Trigonometry deals with the relationships between the sides and angles of triangles.
Understanding angles is crucial in trigonometry basics.
Main functions include sine, cosine, and tangent.
They have applications in fields like physics, engineering, and even computer graphics.
Learning how to convert between radians and degrees will give you better insight into how trigonometric functions operate.
It's also useful to remember the unit circle, where angles are often measured in radians, and key angles like \( \frac{\text{蟺}}{6}, \frac{\text{蟺}}{4}, \) and so on, directly relate to specific degree measures (e.g., 30掳, 45掳).

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Most popular questions from this chapter

A central angle in a circle of radius \(2 \mathrm{~cm}\) cuts off an arc of length \(4.6 \mathrm{~cm}\). What is the measure of the angle in radians? What is the measure of the angle in degrees?

Find the area of the sector for the given radius \(r\) and arc length \(s\). \(r=a, s=a\)

Find the area of the sector for the given angle \(\theta\) and radius \(r\). \(\theta=2.1 \mathrm{rad}, r=1.2 \mathrm{~cm}\)

Find the perimeter of a regular dodecagon (i.e. a 12-sided polygon with sides of equal length) inscribed inside a circle of radius \(\frac{1}{2}\). Compare it to the circumference of the circle.

Convert the given angle to radians. \(130^{\circ}\)
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