# If blahblah, Find the exact value of

• Dec 5th 2010, 08:11 PM
jonoe
If blahblah, Find the exact value of
if sina=12/13 and pi/2 < a < pi, cosB= -4/5 and pi < B < 3pi/2, find the exact value of,

a) sin(a+B)
b)cos(a+B)
c) tan(a+B)

Could someone please explain how to do this? ^^
• Dec 5th 2010, 08:25 PM
Prove It
Remember that $\displaystyle \sin^2{\theta} + \cos^2{\theta} = 1$.

You can use this fact to find the values of $\displaystyle \cos{a}$ (remembering that it is in the second quadrant) and $\displaystyle \sin{B}$ (remembering that it is in the third quadrant).

Using these, you can find the tangent values using $\displaystyle \tan{\theta} = \frac{\sin{\theta}}{\cos{\theta}}$.

Then use the identities

$\displaystyle \sin{(\alpha \pm \beta)} = \sin{\alpha}\cos{\beta} \pm \cos{\alpha}\sin{\beta}$

$\displaystyle \cos{(\alpha \pm \beta)} = \cos{\alpha}\cos{\beta} \mp \sin{\alpha}\sin{\beta}$

$\displaystyle \tan{(\alpha \pm \beta)} = \frac{\tan{\alpha} \pm \tan{\beta}}{1 \mp \tan{\alpha}\tan{\beta}}$.
• Dec 5th 2010, 08:29 PM
jonoe
Thanks a lot.