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Which of the following is equivalent to cos of 40 degrees?
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Is it A) negative sin of 40 degrees, B) sin of 40 degrees, C) one over sin of 40 degrees, D) sin of 50 degrees, or E) sin of 140 degrees.
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We have been given an expression in terms of cos and five solutions in terms of sin.
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So let’s recall what we know about the relationship between the cosine and sine functions.
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There are two that spring to mind.
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For an angle 𝑥 degrees, sin of 90 minus 𝑥 is equal to cos of 𝑥.
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And cos of 90 minus 𝑥 is equal to sin of 𝑥.
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These are two correlated angle identities that we need to know by heart.
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So how did this help us and which one do we choose?
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Well, we’ve been given cos of 40 degrees.
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And there’re two ways we could go about this.
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We could say that that’s the same as cos of 90 minus 50 degrees since 90 minus 50 is 40.
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And then, we use the second identity.
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This says that cos of 90 minus 𝑥 is the same as sin of 𝑥.
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So this means that cos of 90 minus 50 is the same as sin of 50 degrees.
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And that’s D.
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Cos of 40 degrees is equal to sin of 50 degrees.
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Now actually, we could’ve used the first identity too.
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This way says that sin of 90 minus 𝑥 is equal to cos of 𝑥.
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So sin of 90 minus 40 is just equal to cos of 40.
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And we then see that cos of 40 degrees once again is equal to sin of 50 degrees.