Question

what is tan(alpha + beta)
tan of alpha = -3/4
tan of beta = -5/12

Answer 1

\[\tan (\alpha +\beta) = \frac{ (\tan \alpha + \tan \beta) }{ 1-\tan \alpha \tan \beta }\]

Answer 2

Okay, so you have the formula, now sub in your values of alpha and beta for your answer.

Answer 3

I plugged it in but idk how to like do the basic math, I forgot sadly

Answer 4

\[\frac{ -\frac{ 3 }{ 4 } - \frac{ 5 }{ 12 } }{ 1- (-\frac{ 3 }{ 4 }*-\frac{ 5 }{ 12 } )}\]

Answer 5

so then I end up with something like
\[\frac{ -\frac{ 15 }{ 48 } }{ 1+\frac{ 15 }{ 48 } }\]

Answer 6

Then I get stuck

Answer 7

i messed up the numerator

Answer 8

numerator is \[\frac{ 7 }{ 6 }\]

Answer 9

negative 7/6

Answer 10

Great! At least you've given it a go. Your numerator is now correct :) Your denominator is incorrect though, be careful of the negative sign on the bottom. Do you see your mistake?

Answer 11

\[1-\frac{ 15 }{ 48 }\]?

Answer 12

Yeah, exactly! So we now have \[\frac{-\frac{7}{6}}{1-\frac{15}{48}} \]

Answer 13

Can you simplify the denominator: \[1-\frac{15}{48} \]

Answer 14

oh \[\frac{ 33 }{ 48 }\]

Answer 15

Exactly, and that simplifies to: \[\frac{11}{16} \]So we now have: \[\frac{-\frac{7}{6}}{\frac{11}{16}} \]Do you know what to do when dividing something by a fraction?

Answer 16

not at all, clueless

Answer 17

You multiply by the reciprocal (upside down) of that fraction. So for example

\[\frac{\frac{a}{b}}{\frac{c}{d}} = \frac{ad}{bc}\]