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Weird trig 3

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Weird trig 3 Weird trig 3 Presentation Transcript

  • Weird Trigonometry (3) By Dave C, 2013
  • Tan(x) Cos(x) 1.2 Find x between 0 and 90 degrees
  • Tan(x) Cos(x) 1.2 Find x between 0 and 90 degreesThe angle could be big, moderate or small.If the angle is big, then the Tan value will be bigger than 1 andthe cosine will be close to 0. Therefore the Tan can’t be biggerthan 1.2, which limits its size to about 50 degrees. In that case,the Cos is not close to 0. That’s a contradiction, which tells youthat the angle can’t be big.
  • Tan(x) Cos(x) 1.2 Find x between 0 and 90 degreesThe angle could be big, moderate or small.If the angle is moderate, then the Tan is close to 1 and the Cosis close to 0.7. This is still too big. Therefore the angle must besmall.
  • Tan(x) Cos(x) 1.2 Find x between 0 and 90 degreesThe angle could be big, moderate or small.If the angle is small, then the Tan is small and the Cos is closeto 1. That implies that the Tan is close to 0.2, which isconsistent with the assumption. Since this works, try a smallangle.
  • Tan(x) Cos(x) 1.2Tan(x) xCos(x) 1 x 1 1.2 x 0.2 (rads) x 11.4O (degrees)
  • Tan(x) Cos(x) 1.2Test Tan(11.4 O ) Cos(11.4 O ) 1.18 ( Good enough for me ) x 11.4O (degrees)
  • Tan(x) Cos(x) 1.2Solving this the ‘proper’ way would require a unifying transform,something like the t formula. 2t 1- t 2 1.2 1- t 2 1 t2Solving this without a calculator or spreadsheet would be... er..‘challenging’ to say the least.
  • [END]