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Find the value of the cos of 11𝜋 over six.
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We begin by noticing that our angle is given in radians, and we recall that 𝜋 radians is equal to 180 degrees.
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Dividing both values by six, we see that 𝜋 over six radians is equal to 30 degrees.
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We can then multiply both sides of this equation by 11, showing us that 11𝜋 over six radians is equal to 330 degrees.
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This means that the value we need to calculate is the cos of 330 degrees.
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We can do this by firstly sketching the graph of the cosine function and then using our knowledge of special angles.
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The cosine function is periodic and has a maximum value of one and a minimum value of negative one.
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The graph of 𝑦 equals cos of 𝜃 between zero and 360 degrees is shown.
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We want to calculate the cos of 330 degrees.
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From our graph, we can see that this is positive and lies between zero and one.
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Due to the symmetry of the cosine function, we can see from our graph that the cos of 330 degrees is equal to the cos of 30 degrees.
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One of the special angles we need to recall is that the cos of 30 degrees is equal to root three over two.
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This means that the cos of 330 degrees is also equal to root three over two.
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The cos of 11𝜋 over six radians is, therefore, also equal to root three over two.