WEBVTT
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Which of the following expressions is equivalent to one over sec π?
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The options are sin π, cos π, tan π, cot π, or cosec π.
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We will begin by recalling what is meant by sec of π.
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Sec of π is one of our reciprocal trigonometric functions.
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Itβs defined as the reciprocal of cos π.
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Thatβs one over cos π.
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So the expression weβve been given in the question, which is one over sec of π, means one divided by one over cos π.
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We recall that, to divide by a fraction, we flip or invert that fraction.
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And then, we multiply.
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So one divided by one over cos π is equal to one multiplied by cos π over one.
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This just simplifies to cos of π.
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So this is our answer for which expression is equivalent to one over sec π.
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In fact, we couldβve worked this out without doing the division because reciprocal relationships work both ways.
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If sec π is the reciprocal of cos π, then cos π is also the reciprocal of sec π.
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So one over sec π is equal to cos π.
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Letβs just recall what is meant by two of the other options we were given, cot of π and cosec of π, which are the reciprocal trigonometric functions of tan π and sin π, respectively.
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To help you remember which reciprocal trigonometric function belongs with which trigonometric function, we could look at the third letters.
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For example, the third letter of cot is t.
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And cot of π is equal to one over tan π.
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The first letter of tan is also t.
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This same method works for cosec of π, which is equal to one over sin π, and sec of π, which is equal to one over cos of π.
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Our answer to which expression is equivalent to one over sec π is cos π.