Worked Problems
Converting Degrees to Radians
Tip 1:
Make sure you set up the dimensional analysis to cancel out the units you’re converting from and leave your desired units. For example, if you’re converting from degrees to radians, put the degrees in the denominator and radians in the numerator.
Problem #1
Convert 56˚ to radians. Reduce to lowest terms.
How I Solve This
I solve this in three steps.
Step 1: Set Up Dimensional Analysis.
From the equivalence π rad = 180˚, I’ll set up the analysis as follows so that the degrees cancel out and leave the radians:
56˚ • π rad/180˚
Step 2: Simplify.
I’ll simplify the fraction and reduce to lowest terms if possible.
56˚ • π rad/180˚ = 56π/180 rad = 14π/45 rad
Step 3: Answer.
In lowest terms, 56˚ = 14π/45 rad.
Extra Step (For A+ Students): Check.
I check my answer by substituting 180 in for π and simplifying.
14(180)/45 = 14(4) = 56
My answer is correct.
Problem #2
Convert 6π/7 radians to degrees. Round to the nearest degree.
How I Solve This
I solve this very similarly to the previous problem, again in 3 steps.
Step 1: Set Up Dimensional Analysis.
From the equivalence 180˚ = π, I set up the analysis as follows so that the radians cancel out to leave the radians:
6π/7 rad • 180˚/π rad
Step 2: Evaluate.
I use a calculator to evaluate 6(180)/7 and round to the nearest degree.
6(180)/7 ≈ 154
Step 3: Answer.
To the nearest degree, 6π/7 rad = 154˚.
Extra Step (For A+ Students): Check.
I check my answer by dividing 154 by 180 and checking to see if that equals 6/7 (here, approximately because 154 is rounded).
154/180 ≈ 0.86 ≈ 6/7
My answer is correct.
Summary of My Method
To solve these kinds of problems, I follow 3 steps:
- Set Up Dimensional Analysis: I set up the dimensional analysis so that the degrees or radians (depending on the problem) cancel and leave my desired units.
- Simplify: I simplify the fractions to get the final answer.
- Answer: I write the answer with the correct units.
Also, I make sure to check my answers to ensure I calculated correctly.
If you have any questions or would like some help with problems like these, feel free to send me a message. I hope these calculations will help you as you continue on your journey of math mastery 🙂
~ Your Humble Study Buddy,
Ace
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