In Exercises 1–6, use the figures to find the exact value of each...

Question

In Exercises 1–6, use the figures to find the exact value of each trigonometric function.

tan 2α

Accepted Answer

Hello, everyone. We are asked to determine the exact value of the trigonometric function. Using the provided figure. We are given a right triangle where the hypotenuse measures 61. The leg across from angle delta measures 11 and the leg adjacent to angle delta measures 60. We want to find the value of the tangent of two delta. We are given four answer choices. The first thing to recall is that when working with a double ale identity, the tangent of two delta is the same as two multiplied by the tangent of delta divided by one minus the tangent squared of delta. So in order to use this identity, we first must find the value for the tangent of delta. So recall that the ratio for tangent is the opposite leg divided by the adjacent leg. So here, opposite delta, we have 11 and adjacent to delta, we have 60. So tangent of delta is 11 60th. So we're gonna plug this into our identity for the tangent of two delta. So we'll have two multiplied by the tangent of delta. So 11 60th as a numerator and then our denominator is one minus and it's gonna be the tangent squared of delta. So 11 60th squared multiplying my num reader, I end up with 22 60th in the denominator. I'm going to square the 11 60th, the one minus stays put. So I end up with 121 divided by 3600. I'm gonna leave my numerator as it is for now. So 22 divided by 60 and I'm going to do one minus 121 over 3600 by making a common denominator and subtracting which will give me 3479 divided by 3600. I'm going to rewrite my complex fraction as fractions divided. So 22 divided by 60 divided by 3479 divided by 3600. Recalling my rules of fractions. I know that this is the same as multiplying by the reciprocal. So 22/60 times or multiplied by 3600 divided by 3479. I'm going to cross reduce, I know that I can reduce 60 with 3600 and I know that 60 goes into 3660 times. So this means I'm gonna multiply my num readers 22 multiplied by 60 will give me 1320. The denominators one multiplied by remains 3479. So the exact value of two del or sorry of tangent of two delta is 1320 divided by 3479. And that is answer choice C have a nice day.

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In Exercises 1–6, use the figures to find the exact value of each trigonometric function.
tan 2α