An angle is given to one significant figure as 7 degrees

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SUMMARY

The discussion centers on determining the range of possible values for the cosine of an angle given as 7 degrees, which is expressed with one significant figure. The angle's true value lies between 6.5 degrees and 7.5 degrees. The cosine values for these angles are calculated, revealing that cos(6.5) is approximately 0.923 and cos(7.5) is approximately 0.991. This indicates that the cosine value ranges from 0.923 to 0.991, demonstrating that the result contains more significant figures than the input data.

PREREQUISITES
  • Understanding of trigonometric functions, specifically cosine.
  • Knowledge of significant figures and their implications in calculations.
  • Familiarity with angle measurement in degrees.
  • Basic calculator proficiency for evaluating trigonometric functions.
NEXT STEPS
  • Calculate cosine values for angles using a scientific calculator.
  • Explore the concept of significant figures in mathematical results.
  • Learn about the implications of rounding in trigonometric calculations.
  • Investigate the behavior of cosine functions in different quadrants.
USEFUL FOR

Students studying trigonometry, educators teaching mathematical concepts, and professionals in fields requiring precise calculations involving angles and trigonometric functions.

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An angle is given to one significant figure as 7 degrees, meaning that's its value is between 6.5 degrees and 7.5 degrees. Find the corresponding range of possible values of the cosine of the angle. Is this a case in which there are more significant figures in the result than in the input data?

I know the answer to the last question is yes. When I type in [tex]cos(7)[/tex] I get 0.9925461516. Would I round this up to 1 degree, thus its range of values is between 0.5 degrees and 1.5 degrees?

thanks
 
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The angle is between 6.5 and 7.5 degrees, but you aren't sure. It's asking you to find what range the cosine of that angle lies in.
 
The largest the angle can be is 7.5 degrees. What is the cosine of 7.5 degrees?

The smallest the angle can be is 6.5 degrees. What is the cosine of 6.5 degrees?

Now, what do YOU think the possible range for cosine is? You may notice that some of the digits in the two answers are the same. What would be a good way of reporting a single number to represent that range?
 

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