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hram777 [196]
2 years ago
5

Find an exact value cos(19pi/12)

Mathematics
2 answers:
lions [1.4K]2 years ago
6 0
19 π / 12 = 19 * 180° / 12 = 285 °
cos ( 19 π / 12 ) = cos 285° = cos ( - 75° ) = cos 75°
cos 75° = cos ( 45° + 30° ) = cos 45° cos 30° - sin 45° sin 30° =
= ( √2 / 2 · √3/2 ) - ( √2 / 2 · 1/2 ) = √6/4  - √2/4 =
= ( √6 - √2 )/ 4
dmitriy555 [2]2 years ago
3 0

cos\left ( \frac{9\pi}{12}\right )=\frac{\sqrt{2-\sqrt{3}}}{2}

Step-by-step explanation:

We know that

          cos 2x = 2cos²x - 1

So we have

          cosx=\sqrt{\frac{1+cos2x}{2}}

Substituting x=\frac{19\pi}{12}

         cos\left ( \frac{19\pi}{12}\right )=\sqrt{\frac{1+cos2\left ( \frac{19\pi}{12}\right )}{2}}\\\\cos\left ( \frac{19\pi}{12}\right )=\sqrt{\frac{1+cos\left ( \frac{19\pi}{6}\right )}{2}}\\\\cos\left ( \frac{9\pi}{12}\right )=\sqrt{\frac{1+cos570}{2}}\\\\cos\left ( \frac{9\pi}{12}\right )=\sqrt{\frac{1-\frac{\sqrt{3}}{2}}{2}}\\\\cos\left ( \frac{9\pi}{12}\right )=\sqrt{\frac{2-\sqrt{3}}{4}}\\\\cos\left ( \frac{9\pi}{12}\right )=\frac{\sqrt{2-\sqrt{3}}}{2}

   cos\left ( \frac{9\pi}{12}\right )=\frac{\sqrt{2-\sqrt{3}}}{2}

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Please work out and explain​
Mekhanik [1.2K]

Answer:

a = 22

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Step-by-step explanation:

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One of the diagonals is already complete.  The sum is:

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