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Hello everybody.
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In this video, i'm going to be showing you how to solve exercise 19 in chapter 9, section 1 of cohen's pre -calculus 7th edition.
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Now, in this problem, they want us to use the first edition formula for sign to compute the quantity, sign of 7 pi over 12.
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Now, to begin, what we want to do is recognize that this argument, 7 pi over 12, is equal to 4 pi over 12 plus 3 pi over 12.
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And both of these fractions can be reduced to the fractions, pi over 3, as well as pi over 4.
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And so we have that 7 pi over 12 is equal to pi over 3 plus pi over 4.
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And this is important because individually each of these fractions can be evaluated explicitly when plugged in to sine and cosine.
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Now the next thing we want to do is recall the first edition formula for sign, which deals with additions in its argument.
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For two angles, s and t, the sine of s plus t is equal to the sine of s times the cosine of t plus the cosine of t plus the cosine of s times the sine of t.
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So now what we can do is in the left -hand side of this formula, we can go ahead and plug in s equals pi over 3 and t equal to pi over 4.
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And what this gives us is the sign of pi over 3 plus pi over 4.
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And as we saw in the calculation that we did at first, pi over 3 plus pi over 4 is just equal to 7 pi over 12...