Understanding Trigonometric Functions: Solving for Length AD

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SUMMARY

The discussion centers on calculating the length AD using trigonometric functions, specifically 8sin20° and 8cos70°. The user initially believed both calculations would yield the same result but discovered discrepancies due to their calculator being set to radians instead of degrees. The correct values are 8cos70° = 5.067 and 8sin20° = 7.304, confirming that the calculations are indeed different. Additionally, it is noted that cos70° must be less than 0.5, reinforcing the understanding of trigonometric values in relation to angles.

PREREQUISITES
  • Understanding of basic trigonometric functions (sine and cosine)
  • Familiarity with angle measurement in degrees and radians
  • Ability to use a scientific calculator
  • Knowledge of the unit circle and its properties
NEXT STEPS
  • Learn how to convert between degrees and radians in trigonometric calculations
  • Study the unit circle and its application in solving trigonometric problems
  • Explore the properties of sine and cosine functions for various angles
  • Practice using a scientific calculator effectively for trigonometric functions
USEFUL FOR

Students studying trigonometry, educators teaching mathematical concepts, and anyone needing to solve problems involving angles and lengths using trigonometric functions.

smulc
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I need to find the length AD. I thought that with the numbers given, and angle A worked out to being 70o there would be two different ways of working length AD out. I thought 8sin20 and 8cos70 would both be acceptable ways of calculating the length but they give different values. Where have I gone wrong?

Thanks.
 

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They don't give different values.
 
My calculator gives 8cos70 = 5.067 and 8sin20 = 7.304.
 
just realized it was in raidians mode. Whoops!
 
smulc said:
My calculator gives 8cos70 = 5.067 and 8sin20 = 7.304.

and you should realize (hopefully quickly) that if cos60o=1/2 then cos70o must be less than half, so there is no way 8cos70o > 5, and similarly with sin20o :wink:
 

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