In Exercises 31–38, find a cofunction with the same value as the ...

Question

In Exercises 31–38, find a cofunction with the same value as the given expression.tan 𝜋9

Accepted Answer

Hello everybody. I have everything right today that we're going to begin this question that states which of the following core functions has the same value as tangents of open parentheses. Three pi divided by 13 closed parentheses where our answer choices are a code tangents of open parentheses. Two pi divided by 13 closed parentheses. B code tangents of open parentheses. Seven pi divided by 26 closed parentheses. C co tangents of open parentheses. Seven pi divided by 13 closed parentheses and the cotangent of open parentheses, five pi divided by 26 closed parentheses. No, we know that tangent and cotangent are co functions here. So what is their rule? Well, let's recall that tangent data is equal to cotangent of pi divided by two minus beta. So that is how you can switch between tangent and co tangent. So now let's use that with our numbers. So we have tangents of three pi divided by 13 will be equal to co tangents of open parentheses. Pi divided by two minus three pi divided by 13 closed parentheses. So let's focus on the Coltan part and the subtraction first, we want to get a similar denominator in both fractions. So we'll have co tangents of open parentheses. 13 pi divided by 26. And what I did here was multiply the numerator and denominator by 13. So we have 13 pie in deer and 26 pi in the denominator minus. Now we have six pie divided by 26. And what I did for that fraction was multiply the numerator and denominator by two. So now we have a common denominator and we can go ahead and subtract and we'll have co tangent 13, they have a common nominator. So all we have to subtract is the numerator 13 minus six is seven. So we have coal tangent of seven pi divided by 26. And that will be the co function with the same value as the one that we were given or in this case, answer choice B. So I hope that was helpful. And until next time.

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In Exercises 31–38, find a cofunction with the same value as the given expression.tan 𝜋9

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