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vitfil [10]
2 years ago
12

Express the product of cos 30°and 45° in simple simplest radical form

Mathematics
2 answers:
dem82 [27]2 years ago
7 0
cos30^0=  \frac{ \sqrt{3} }{2} \ \ \ and\ \ \ cos45^0= \frac{ \sqrt{2} }{2}\\\\cos30^0\cdot cos45^0= \frac{ \sqrt{3} }{2}\cdot \frac{ \sqrt{2} }{2}= \frac{ \sqrt{3} \cdot \sqrt{2} }{2\cdot 2}=\frac{ \sqrt{6} }{4}
Advocard [28]2 years ago
7 0
This means the multiplication of the cos of the particular angles

cos(30^{o}) = \frac{ \sqrt{3} }{2} , cos(45^{o}) = \frac{ \sqrt{2} }{2}


So, multiplying them together is 

= \frac{ \sqrt{3} }{2} *\frac{ \sqrt{2} }{2} = \frac{ \sqrt{6} }{4}
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Step-by-step explanation:

A diagram can help you understand the question, and can give you a clue as to how to find the answer. A diagram is attached. The problem can be described as finding the sum of two vectors whose magnitude and direction are known.

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<h3>understanding the direction</h3>

In navigation problems, direction angles are specified a couple of different ways. A <em>bearing</em> is usually an angle in the range [0°, 360°), <em>measured clockwise from north</em>. In land surveying and some other applications, a bearing may be specified as an angle east or west of a north-south line. In this problem we are given the bearing of the second leg of the walk as ...

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Occasionally, a non-standard bearing will be given in terms of an angle north or south of an east-west line. The same bearing could be specified as E 55° N, for example.

<h3>the two vectors</h3>

A vector is a mathematical object that has both magnitude and direction. It is sometimes expressed as an ordered pair: (magnitude; direction angle). It can also be expressed using some other notations;

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Sometimes a semicolon is used in the polar coordinate ordered pair to distinguish the coordinates from (x, y) rectangular coordinates.

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The first leg of the walk is 3 meters due north. The angle from north is 0°, and the magnitude of the distance is 3 meters. We can express this vector in any of the ways described above. One convenient way is 3∠0°.

The second leg of the walk is 2.5 meters on a bearing 35° clockwise from north. This leg can be described by the vector 2.5∠35°.

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The final position is the sum of these two changes in position:

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Some calculators can compute this sum directly. The result from one such calculator is shown in the second attachment:

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This tells you the magnitude of the distance from the original position is about 5.25 meters. (This value is also shown in the first attachment.)

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The distance from the original position is about 5.25 meters.

_____

<em>Additional comment</em>

The vector sum can also be calculated in terms of rectangular coordinates. Position A has rectangular coordinates (0, 3). The change in coordinates from A to B can be represented as 2.5(sin(35°), cos(35°)) ≈ (1.434, 2.048). Then the coordinates of B are ...

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  OB = √(1.434² +5.048²) ≈ 5.248

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