1. ## Help with sum and difference identities, please!

Hi there.

We learned in calc the sum and difference identities:

For the most part it's not too bad, but I'm confused on a couple of problems in my book.

What would tan(a-b) be if sin a = .67, cos a = .74, sin b =.13 and cos b =-.99

The cos of b, if you notice, is negative.

how do I find tan(a + pi)?

what's cos (a + pi/3)?

and what's sin (pi/6 - a)?

Thanks a lot!

2. Hello,
Originally Posted by gobbajeezalus
Hi there.

We learned in calc the sum and difference identities:

For the most part it's not too bad, but I'm confused on a couple of problems in my book.

What would tan(a-b) be if sin a = .67, cos a = .74, sin b =.13 and cos b =-.99
Remember that $\displaystyle \tan(x)=\frac{\sin(x)}{\cos(x)}$
So with the information given, calculate $\displaystyle \tan(a)$ and $\displaystyle \tan(b)$ and substitute in the formula you're given for $\displaystyle \tan(a-b)$

The cos of b, if you notice, is negative.
it doesn't matter :P

how do I find tan(a + pi)?
make $\displaystyle x=a \quad y=\pi$

what's cos (a + pi/3)?
make $\displaystyle x=a \quad y=\pi/3$

and what's sin (pi/6 - a)?
make $\displaystyle x=\pi/6 \quad y=a$ in the sin(x-y) formula.

Now, for these last 3 values, you have to know specific values of trigonometric functions, at some points.

They're "listed" here : http://everobotics.org/projects/robo...UnitCircle.gif