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Chapter 4: Problem 43

Use an inverse trigonometric function to write \(\theta\) as a function of \(x .\)

Short Answer

Expert verified
Depending on the specific equation between \(x\) and \( \theta \), if, for example, \(x = sin(\theta)\), then \(\theta = sin^{-1}(x)\) or \(\theta = asin(x)\).

Step by step solution

01

Identify the trig function to use

Since \(x\) is a trigonometric function of \( \theta \), let's first identify this trigonometric function. Some common examples could be like \(x = sin(\theta)\), \(x = cos(\theta)\), \(x = tan(\theta)\) etc. To proceed further, we will have to know the specific trigonometric relation between \(x\) and \( \theta \). Let's assume for the sake of this example, it's \(x = sin(\theta)\). This assumption should be replaced with the actual equation provided in the specific problem.
02

Apply the inverse trig function

Once you have identified the trigonometric function, you can rewrite the equation by applying the inverse trigonometric function. The inverse of sine function is arcsine (usually written as \(sin^{-1}\) or asin), cosine is arccosine (\(cos^{-1}\) or acos), and tangent is arctangent (\(tan^{-1}\) or atan). So in this case, since we assumed \(x = sin(\theta)\), \( \theta \) would be expressed in terms of \(x\) as \(\theta = sin^{-1}(x)\) or \(\theta = asin(x)\).

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Use an inverse trigonometric function to write \(\theta\) as a function of \(x .\)

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