How Should You Correctly Input Trigonometric Ratios in a Calculator?

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SUMMARY

The correct input for trigonometric ratios in a calculator depends on the placement of parentheses in the equation. The discussion centers on the equation θ = Sin^{}-1(0.6/3). When entered without parentheses, the calculator returns 12.29, while using parentheses yields 11.54. The accurate interpretation is to use θ = Sin^{}-1(0.6/3), which indicates that the calculation should be performed on the fraction first before applying the inverse sine function.

PREREQUISITES
  • Understanding of trigonometric functions, specifically inverse sine (arcsin).
  • Familiarity with calculator operations, including the use of parentheses.
  • Basic knowledge of fractions and their manipulation.
  • Experience with solving tension queries in physics or engineering contexts.
NEXT STEPS
  • Research the properties of inverse trigonometric functions, particularly arcsin.
  • Learn about calculator syntax for trigonometric functions and the importance of parentheses.
  • Explore examples of tension calculations in physics involving trigonometric ratios.
  • Study the implications of order of operations in mathematical expressions.
USEFUL FOR

Students in physics or engineering, educators teaching trigonometry, and anyone needing to perform accurate trigonometric calculations using calculators.

junkie_ball
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Hi,

I have a simple question i am working a tension query and need to do some trig calculations. I know the equation i need is below.

θ = Sin^{}-1 0.6/3

When i type this in the calculator as shown above i get an answer of 12.29 although when i enter it in the calculator using brackets around (0.6/3) i then get an answer of 11.54 which one would be correct? I just need to ensure i am entering into the calculator correctly.
 
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junkie_ball said:
Hi,

I have a simple question i am working a tension query and need to do some trig calculations. I know the equation i need is below.

θ = Sin^{}-1 0.6/3

When i type this in the calculator as shown above i get an answer of 12.29 although when i enter it in the calculator using brackets around (0.6/3) i then get an answer of 11.54 which one would be correct? I just need to ensure i am entering into the calculator correctly.
The answer depends upon whether you are looking for (sin^{-1}0.6)/3 or sin^{-1}(0.6/3) I suspect you are looking for the latter, are you??
 

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