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Anna007 [38]
3 years ago
8

How many significant figures are in the measured value 550,000,000?

Mathematics
1 answer:
NikAS [45]3 years ago
5 0

There are 2 significant figures (sig figs) which are the two '5' digits. The zeros aren't considered sig figs because we can write the number as 5.5 * 10^8 to represent the exact same idea. The 0's are simply placeholders to tell how big the number is, not necessarily how accurate it is. If the 0s were between the decimal point and a nonzero value, then the 0s would be significant. If the 0s were to the right of the decimal, then they would be significant.

Answer: 2

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Given tan theta =9, use trigonometric identities to find the exact value of each of the following:_______
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Answer:

(a)\ \sec^2(\theta) = 82

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Step-by-step explanation:

Given

\tan(\theta) = 9

Required

Solve (a) to (d)

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\tan(\theta) = \frac{Opposite}{Adjacent}

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So, we have:

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Hypotenuse =\sqrt{82}

Solving (a):

\sec^2(\theta)

This is calculated as:

\sec^2(\theta) = (\sec(\theta))^2

\sec^2(\theta) = (\frac{1}{\cos(\theta)})^2

Where:

\cos(\theta) = \frac{Adjacent}{Hypotenuse}

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So:

\sec^2(\theta) = (\frac{1}{\cos(\theta)})^2

\sec^2(\theta) = (\frac{1}{\frac{1}{\sqrt{82}}})^2

\sec^2(\theta) = (\sqrt{82})^2

\sec^2(\theta) = 82

Solving (b):

\cot(\theta)

This is calculated as:

\cot(\theta) = \frac{1}{\tan(\theta)}

Where:

\tan(\theta) = 9 ---- given

So:

\cot(\theta) = \frac{1}{\tan(\theta)}

\cot(\theta) = \frac{1}{9}

Solving (c):

\cot(\frac{\pi}{2} - \theta)

In trigonometry:

\cot(\frac{\pi}{2} - \theta) = \tan(\theta)

Hence:

\cot(\frac{\pi}{2} - \theta) = 9

Solving (d):

\csc^2(\theta)

This is calculated as:

\csc^2(\theta) = (\csc(\theta))^2

\csc^2(\theta) = (\frac{1}{\sin(\theta)})^2

Where:

\sin(\theta) = \frac{Opposite}{Hypotenuse}

\sin(\theta) = \frac{9}{\sqrt{82}}

So:

\csc^2(\theta) = (\frac{1}{\frac{9}{\sqrt{82}}})^2

\csc^2(\theta) = (\frac{\sqrt{82}}{9})^2

\csc^2(\theta) = \frac{82}{81}

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