# Trig identities help!

• Jul 14th 2008, 11:42 AM
Dave19
Trig identities help!
a stands for alpha b stands for beta

If sin a= -8/17 and a is in the 4th quadrant angle, and tan b= 3/4 and 180degrees is less than or equal to b, and b is less than or equal to 270degrees find the values of each of the following:

a) cos a b) tan a c) sin b d) cos b e) cos(a+b) f) sin(a-b)

g) tan(b-a) h) sin2b i) tan2a j) cos2a k) sin a/2

l) tan b/2
• Jul 14th 2008, 01:33 PM
topsquark
Quote:

Originally Posted by Dave19
a stands for alpha b stands for beta

If sin a= -8/17 and a is in the 4th quadrant angle, and tan b= 3/4 and 180degrees is less than or equal to b, and b is less than or equal to 270degrees find the values of each of the following:

a) cos a b) tan a c) sin b d) cos b e) cos(a+b) f) sin(a-b)

g) tan(b-a) h) sin2b i) tan2a j) cos2a k) sin a/2

l) tan b/2

You know that
a) $\displaystyle sin^2(\theta) + cos^2(\theta) = 1$
You can find the magnitude of cos(a). You also know that a is in QIV, so what does that mean for the sign of cos(a)?

b) You now know sin(a) and cos(a), how do you find tan(a)?

Do d) next.
$\displaystyle tan^2(\theta) + 1 = sec^2(\theta)$
You can find sec(b) from this. (Remember that b is in QIII.) How does sec(b) relate to cos(b)?

c) You can use the sin squared equation here, or recall how tan(b) is defined in terms of sin(b) and cos(b) (and then use d).)

For the rest see here. You are looking specifically for the "Angle Sum and Difference Identities" and the "Double, Triple, and Half-Angle Formulae" sections.

-Dan