Sum Difference Identities

cokeclassic · #1 $Old$ 11-17-2008, 06:51 PM

There is a section on my worksheet that says
"Rewrite each expression in terms of the sine, cosine, or tangent using the addition and subtraction identities. Simplify each result."

I don't understand what I am suppose to do for that section.
first two problems:
sin(5pi/2 + t)

cos (pi/6-t)

and one more thing for another section i am suppose to be finding sin2t cos2t and tan2t

if sin t = 4/5, t in Q I
is this correct
sin2t = 8/5

cost2t = 6/5

tan2t = 8/3???

thanks in advance

skeeter · #2 $Old$ 11-17-2008, 07:43 PM

do you know the sum/difference identities for sine, cosine, and tangent ? they should be listed in your text.

$\sin\left(\frac{5\pi}{2} + t\right) = \sin\left(\frac{5\pi}{2}\right)\cos(t) + \cos\left(\frac{5\pi}{2}\right)\sin(t) = (1) \cdot \cos(t) + (0) \sin(t) = \cos(t)$

look up the difference identity for cosine and determine $\cos\left(\frac{\pi}{6} - t\right)$

if $\sin(t) = \frac{4}{5}$ , then $\sin(2t) \neq \frac{8}{5}$

$\sin(2t) = sin(t+t)$ ... use the sum identity for sine to determine the double angle identity for sine.