Question

cos(θ) = 33/65 where 0 < θ < π/2
sin θ/2=
cos θ/2=

Answer 1

same as before http://openstudy.com/study#/updates/528d7493e4b0fd0888879dc5

Answer 2

you're in the 1st Quadrant this time, thus sine and cosine will both be positive

use the pythagorean theorem to find side "b"

once you have "a", "b" and "c", use the half-angle identities for sine and cosine and plug in your sine and cosine values for \(\theta\)

Answer 3

yeah, i know what to do but my answer isn't right

Answer 4

hnmmm

Answer 5

yeah

Answer 6

actually, I just recall, you don't even need to do all that, since both half-angle identities just use cosine....

Answer 7

yeah, i used 33/55 and still didn't get the right answer

Answer 8

one sec

Answer 9

okay

Answer 10

\(\bf cos(\theta)=\cfrac{33}{65}\qquad \qquad \pi<\theta < \frac{\pi}{2}\\ \quad \\
sin\left(\frac{\theta}{2}\right)=\sqrt{\cfrac{1-cos(\theta)}{2}}\implies sin\left(\frac{\theta}{2}\right)=\sqrt{\cfrac{1-\frac{33}{65}}{2}}\\ \quad \\
sin\left(\frac{\theta}{2}\right)=\sqrt{\cfrac{\frac{32}{65}}{2}}\implies sin\left(\frac{\theta}{2}\right)=\sqrt{\cfrac{16}{65}}\implies sin\left(\frac{\theta}{2}\right)=\cfrac{\sqrt{16}}{\sqrt{65}}\\ \quad \\
sin\left(\frac{\theta}{2}\right)=\cfrac{4}{\sqrt{65}}\implies sin\left(\frac{\theta}{2}\right)=\cfrac{4}{\sqrt{65}}\cdot \cfrac{\sqrt{65}}{\sqrt{65}}\implies sin\left(\frac{\theta}{2}\right)=\cfrac{4\sqrt{65}}{65}\)

Answer 11

\(\bf cos(\theta)=\cfrac{33}{65}\qquad \qquad \pi<\theta < \frac{\pi}{2}\\ \quad \\ \quad \\
cos\left(\frac{\theta}{2}\right)=\sqrt{\cfrac{1+cos(\theta)}{2}}\implies cos\left(\frac{\theta}{2}\right)=\sqrt{\cfrac{1+\frac{33}{65}}{2}}\\ \quad \\
cos\left(\frac{\theta}{2}\right)=\sqrt{\cfrac{\frac{98}{65}}{2}}\implies cos\left(\frac{\theta}{2}\right)=\sqrt{\cfrac{49}{65}}\implies cos\left(\frac{\theta}{2}\right)=\cfrac{\sqrt{49}}{\sqrt{65}}\\ \quad \\
cos\left(\frac{\theta}{2}\right)=\cfrac{7}{\sqrt{65}}\implies cos\left(\frac{\theta}{2}\right)=\cfrac{7}{\sqrt{65}}\cdot \cfrac{\sqrt{65}}{\sqrt{65}}\implies cos\left(\frac{\theta}{2}\right)=\cfrac{7\sqrt{65}}{65}\)

Answer 12

thanks

Answer 13

yw