Posted by **Lucy** on Saturday, August 30, 2008 at 10:12pm.

How do you work this problem. I cannot find an example in the book to illustrate how to work it.

Find the value of tan(a-b) if cos a=-3/5, sin b=5/13, 90<a<180, and 90<b<180

Thanks for any help

- Pre-Calculus -
**Reiny**, Saturday, August 30, 2008 at 10:48pm
your text should have

tan(a-b) = (tan a - tan b)/(1 + tanatanb)

so you will need tan a and tan b

cos a = -3/5 and a is in the second quadrant, so by sketching a diagram it is easy to see that sin a = 4/5 and

tan a = - 4/3

similarly sin b = 5/13 and b is in quadrant II, so cos b = -12/13 and

tan b = -5/12

then tan(a-b)

=(-4/3 - (5/12))/(1 + (-4/3)(-5/12))

= -33/56

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