Question

sin theta = -4/5
cos beta = -5/13

I have to find cos theta/2 I don't think my final answer is correct so may someone go through it with me

Answer 1

So what did you get for your cos(theta) so far? :o

Answer 2

This problem is confusing, I'm not even sure how the cos(beta) is going to help us...

Answer 3

3/5

Answer 4

Ok good.
And then we use our Half-Angle Identity or something, ya?\[\Large\rm \cos\frac{\theta}{2}=\sqrt{\frac{1+\cos \theta}{2}}\]

Answer 5

Yes

Answer 6

\[\Large\rm \cos\frac{\theta}{2}=\sqrt{\frac{1+\frac{3}{5}}{2}}\]

Answer 7

then I multiplied 5 to he 1 and 2 and left 3

Answer 8

Multiplied by 5?
Like top and bottom by 5?
It should give you something like this if you do that:\[\Large\rm \cos\frac{\theta}{2}=\sqrt{\left(\frac{1+\frac{3}{5}}{2}\right)\frac{5}{5}}\]gives,\[\Large\rm =\sqrt{\frac{5+3}{2\cdot5}}\]

Answer 9

yep

Answer 10

I guess they'll probably want you to rationalize your answer,
so let's do that, it'll look a little nicer getting the square root out of the bottom.

Answer 11

\[\Large\rm =\sqrt{\frac{8}{10}}=\sqrt{\frac{4}{5}}=\frac{\sqrt4}{\sqrt5}\]

Answer 12

We'll multiply top and bottom by sqrt(5), ya?

Answer 13

Yes

Answer 14

sqrt of 4 is 2

Answer 15

\[\Large\rm =\frac{2}{\sqrt{5}}\cdot\frac{\sqrt5}{\sqrt5}=?\]

Answer 16

\[2\sqrt{5}/5\]

Answer 17

Yayyy good job \c:/

Answer 18

Thank you again haha

Answer 19

Maybe we want a plus/minus on the root,
they don't really give us enough information to determine if it should be positive or negative.. hmm

Answer 20

I'm going over a review so I'm trying to make sure everything is right

Answer 21

ah neato ^^