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Chapter 16: Problem 9

If \(\sin \theta=0.7\), what is \(\tan \theta\) ? a) \(0.98\) b) \(0.94\) c) \(0.88\) d) \(0.85\)

Short Answer

Expert verified
a) \(0.98\) b) \(0.94\) c) \(0.88\) d) \(0.85\) Answer: a) \(0.98\)

Step by step solution

01

Understanding the given information

We are given that \(\sin \theta = 0.7\). Our goal is to find the value of \(\tan \theta\).
02

Find the value of \(\cos \theta\)

We can use the Pythagorean identity: \(\sin^2 \theta + \cos^2 \theta = 1\). Since we are given \(\sin \theta = 0.7\), we have \(\cos^2 \theta = 1 - \sin^2 \theta = 1 - (0.7)^2 = 1 - 0.49 = 0.51\) Now, take the square root of the result to find the value of \(\cos \theta\): \(\cos \theta = \sqrt{0.51} \approx 0.71\) (considering the positive square root, as cosine is positive in the first and fourth quadrants and sine is positive in the first and second quadrants)
03

Calculate \(\tan \theta\)

Now that we have the values for \(\sin \theta\) and \(\cos \theta\), we can use the formula \(\tan \theta = \frac{\sin \theta}{\cos \theta}\) to find \(\tan \theta\): \(\tan \theta = \frac{0.7}{0.71} \approx 0.9859\)
04

Compare the answer with the given options

We compare the calculated value of \(\tan \theta\) with the given options: a) \(0.98\) b) \(0.94\) c) \(0.88\) d) \(0.85\) Our calculated value of \(\tan \theta \approx 0.9859\) is closest to option a) \(0.98\). So, the correct answer is a) \(0.98\).

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Most popular questions from this chapter

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