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4.2.1: Resources and Key Concepts
Opening the book…
Key Concepts
Definitions
Minutes and Seconds: A system for measuring fractions of a degree. One minute (\(1'\)) is defined as \(\frac{1}{60}\) of a degree. One second (\(1''\)) is defined as \(\frac{1}{60}\) of a minute, or \(\frac{1}{3600}\) of a degree.
Common Mistakes
Using the Wrong Calculator Mode: Before evaluating any trigonometric function, you must ensure your calculator is set to the correct mode (degree mode for this section). Using the wrong mode will result in incorrect answers.
Rounding Intermediate Steps: Rounding should only be done for the final answer. If you round a value and then use that rounded value in another calculation, the rounding error can propagate and lead to a significantly different and less accurate final result.
Confusing Inverse Functions with Reciprocals: The notation \(\sin^{-1}(x)\) represents the inverse sine, which finds the angle whose sine is \(x\). It does not mean the reciprocal, \(\frac{1}{\sin(x)}\), which is \(\csc(x)\).
Using Rounded Values in Inverse Functions: When finding an angle, you should use the exact ratio if possible. For example, to find the angle whose tangent is \(\frac{77}{136}\), you should compute \(\tan^{-1}\left(\frac{77}{136}\right)\) directly rather than first approximating \(\frac{77}{136}\) as a decimal and then taking the inverse tangent of the rounded decimal.