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The equation for wavelength from a double-slit experiment uses the simplification that theta is...

Question:

The equation for wavelength from a double-slit experiment uses the simplification that {eq}\theta {/eq} is small so that sin {eq}\theta {/eq} = tan {eq}\theta {/eq}.

Up to what angle is this a good approximation when your data has two significant figures? Explain.

Trigonometry

Trigonometry is a branch of mathematics that deals with the study of angles and triangles generating relationships between each of them. In general terms, trigonometric ratios are sine, cosine, tangent, cotangent, secant, and cosecant.

Answer and Explanation: 1

The following graph shows the comparison between the values of {eq}\rm \theta, sin\theta \text{ and } tan\theta {/eq}

The angle will exceed 1% error for the following angles:

{eq}\rm \tan\theta \approx \theta \rightarrow 0.1730\ rad =9.91^{\circ} \\ \sin\theta \approx \theta \rightarrow 0.2441\ rad = 13.99^{\circ} {/eq}


Learn more about this topic:

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What is Trigonometry? - Functions, Formulas & Applications

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Chapter 22 / Lesson 11
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Learn what trigonometry is and what trigonometric functions are. Understand the examples of how to use each function, as well as know the instances when it is useful to use trigonometry.


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