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Sholpan [36]
3 years ago
15

Explain the geographic context for the development of the Crusades.

History
1 answer:
Kay [80]3 years ago
7 0

The wars created a constant demand for supplies and transportation, which resulted in ship-building and the manufacturing of various supplies. After the Crusades, there was a heightened interest in travel and learning throughout Europe, which some historians believe may have paved the way for the Renaissance.

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23. Find the exact value of cos(20) knowing that: *
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Answer:

\cos(2\theta) = 0

Explanation:

Given

\sin(\theta) = -\frac{\sqrt 2}{2}

270^o < \theta < 360^o

Required

\cos(2\theta)

Recall that:

\sin^2(\theta) +  \cos^2(\theta) =1

Substitute: \sin(\theta) = -\frac{\sqrt 2}{2}

(-\frac{\sqrt 2}{2})^2 +  \cos^2(\theta) =1

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

Collect like terms

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

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

\cos(2\theta) is calculated as:

\cos(2\theta) = \cos^2(\theta) - \sin^2(\theta)

So, we have:

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

\cos(2\theta) = \frac{1}{2} - \frac{2}{4}

\cos(2\theta) = \frac{1}{2} - \frac{1}{2}

\cos(2\theta) = 0

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