Question

write an algebraic expression that is equivalent to cos13pi/12 using related acute angles

Answer 1

maybe try \(\frac{13\pi}{12}=\frac{3\pi}{4}=\frac{\pi}{3}\)

Answer 2

oops typo sorry
i meant
\[\frac{13\pi}{12}=\frac{3\pi}{4}+\frac{\pi}{3}\]

Answer 3

then you can use the addition angle formula

Answer 4

hm.. i used the formula \[\cos(\pi + \theta)=-\cos \theta\]
since if i convert \[\frac{ 13\pi }{ 12 }\] into degrees it would be in the third quadrant

Answer 5

this would work right?

Answer 6

forget degrees, it is in the third quadrant because
\[\pi<\frac{13\pi}{12}<\frac{3\pi}{2}\]

Answer 7

ah true alright.

Answer 8

you can evaluate this because
\[\cos(\frac{13\pi}{12})=\cos(\frac{3\pi}{4}+\frac{\pi}{3})\]
\[=\cos(\frac{3\pi}{4})\cos(\frac{\pi}{3})-\sin(\frac{3\pi}{4})\sin(\frac{\pi}{3})\] and we know all of those

Answer 9

oooooooh okay thank you!

Answer 10

yw