Hello, Ashz!

We are given: .

We have: .

Rationalize: .

. . . .

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- Apr 2nd 2012, 02:15 PM #1

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## tan (α-β)

finding the exact value of tan (α-β) when:

tan α = -(5/12) in quad II and cos β = 3/4 and lies in quad I

Triangle α

x = -12

y = 5

r = 13

Triangle β

x = 3

y = √7 (suppose to be square root of 7)

r = 4

tan (α-β) = (tan α - tan ß) / 1 + tan (α) tan (ß)

tan (α-β) = ((-5/12) - (√7/4)) / 1 + (-5/12)(√7/4)

tan (α-β) = ((-5/12) - (3√7/12)) / (48/48) + ((-5√7)/48)

tan (α-β) = ((-5-3√7)/12)((48)/(48-5√7)

tan (α-β) = -1/4 (is what I eventually came up with but it's wrong and I am unsure of what I'm doing wrong...)

I've also added a screen shot of the actual equation just in case the above is too confusing...

- Apr 2nd 2012, 05:30 PM #2

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- Apr 2nd 2012, 06:30 PM #3

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## Re: tan (α-β)

Thanks for replying back ~ but I have 2 additional questions.

1. before we rationalize, how did you get from the tan (α-β) equation to the (-15-12√7)/(36-5√7) ~ you multiplied it the whole equation by 36/36 right?

2. then when you rationalize the equation with 36+5√7 ~ this might be an algebra question, and I've probably forgotten, but why can't you just multiply by 5√7 instead of what you have?

- Apr 3rd 2012, 03:19 AM #4

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- Apr 3rd 2012, 12:39 PM #5

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## Re: tan (α-β)

Sorry but now Im confused ~ bc I thought that you would have to rationalize the denominator if there is a square root there... b/c if I didn't have to rationalize it in the first place, why even bother multiplying it by the 5√7 in the first place... or even the 36+5√7...

- Apr 3rd 2012, 11:22 PM #6

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- Apr 4th 2012, 09:39 AM #7

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## Re: tan (α-β)

I'm sorry, but I think your causing me more confusion on this question Sorban rationalized the answer and I know I didn't post to rationalize the answer, but the attachment I posted showed that it needed to be rationalized. I am prob the one that caused the confusion on this question, but I tried to minimize it with posting the attachment. I think I will just PM Sorban for more information, thanks for your help anyway biffboy. I do appreciate it.