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-BARSIC- [3]
2 years ago
9

If cosх A/2 =3/5, find the value of cos A​

Mathematics
1 answer:
nikitadnepr [17]2 years ago
5 0

Answer:

cosA = - \frac{7}{25}

Step-by-step explanation:

Using the double angle identity

cos2A = 2cos²A - 1 , then

cosA = 2cos²(\frac{A}{2} ) - 1 , that is

cosA = 2 × (\frac{3}{5} )² - 1

        = 2 × \frac{9}{25} - 1

       = \frac{18}{25} - \frac{25}{25}

       = - \frac{7}{25}

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<u><em>Explanation:</em></u>
<u>For shapes to be similar:</u>
1- there should be a ratio between the sides
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Now, a scale factor of 0.2 means that the sides of the image are 0.2 of the length of the original shape. However, angles are not changes

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<u>1- </u><span><u>The corresponding sides of the triangles are congruent:</u>
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<u>2- </u></span><span><u>The corresponding angles of the triangles are congruent:</u>
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<u>3- </u></span><span><u>The corresponding sides of the image are 5 times as long as those of the pre-image:</u>
This option is incorrect as the sides of the image are only 0.2 times as long as those of the pre-image

<u>4- </u></span><span><u>The image is a reduction of the pre-image:</u>
This option is correct as the sides of the image are 0.2 times those of the pre-image which means that the shape is reduced

<u>5- </u></span><span><u>Neither the dilation nor the rotation change the shape of the triangle:</u>
This option is correct as both dilation and rotation are rigid transformations that do not alter the shape of the triangle (a triangle remains a triangle only with different side lengths)

<u>6- </u></span><u>The rotation reduces the size of the triangle:</u>
This option is incorrect as rotation does not alter the size of the shape. It only changes its position

Hope this helps :)

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