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Exercises Trigonometry

Example 8 from Algebra and Trigonometry, 7.1 Angles

Finding the Length of an Arc

Assume the orbit of Mercury around the sun is a perfect circle. Mercury is approximately 36 million miles from the sun.

ⓐ In one Earth day, Mercury completes 0.0114 of its total revolution. How many miles does it travel in one day?
ⓑ Use your answer from part (a) to determine the radian measure for Mercury’s movement in one Earth day.

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

1
Solution
1. ⓐLet’s begin by finding the circumference of Mercury’s orbit.
  $\begin{matrix} C & = & 2 π r \\ = & 2 π (36 million miles) \\ \approx & 226 million miles \end{matrix}$
  Since Mercury completes 0.0114 of its total revolution in one Earth day, we can now find the distance traveled.
  
  $(0.0114) 226 million miles = 2 .58 million miles$
2. ⓑNow, we convert to radians.
  $\begin{matrix} radian & = & \frac{arclength}{radius} \\ = & \frac{2. 58 million miles}{36 million miles} \\ = & 0.0717 \end{matrix}$

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Find the arc length along a circle of radius 10 units subtended by an angle of $215° .$

How did it go?

PreviousFinding Coterminal Angles Using Radians Next Finding the Area of a Sector

From Algebra and Trigonometry (1st edition) by OpenStax (Rice University), section 7.1, licensed under CC BY 4.0. Original at openstax.org. We split the solution into steps; the words, numbers and figures are the book's. OpenStax doesn't endorse this site.