Understanding Trigonometric Functions: Solving for Length AD

  • Context: High School 
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    Trigonometry
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Discussion Overview

The discussion revolves around calculating the length AD using trigonometric functions, specifically exploring the values derived from the sine and cosine of given angles. The scope includes mathematical reasoning and problem-solving related to trigonometry.

Discussion Character

  • Mathematical reasoning, Homework-related

Main Points Raised

  • One participant proposes using 8sin20 and 8cos70 to calculate length AD, believing both methods should yield the same result.
  • Another participant asserts that the two calculations do not yield different values.
  • A participant shares their calculator results, indicating that 8cos70 equals 5.067 and 8sin20 equals 7.304.
  • A later reply reveals that the discrepancy arose from using radians instead of degrees on the calculator.
  • Another participant notes that since cos60° equals 1/2, cos70° must be less than half, suggesting that 8cos70° cannot exceed 5, and similarly for sin20°.

Areas of Agreement / Disagreement

Participants express disagreement regarding the values obtained from the calculations, with some asserting that the results differ while others challenge this claim. The discussion remains unresolved regarding the correctness of the initial calculations.

Contextual Notes

There is a mention of a potential error due to calculator mode (radians vs. degrees), which may affect the results. The implications of trigonometric function values based on angle measures are also discussed.

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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