Question

cos theta=-4/5 and 90 degrees< theta< 180.
Find cos theta/2

Answer 1

First of all apply this:

\[\large{\cos(2x) = 2\cos^2(x) - 1}\]

Answer 2

I have no clue how to do that.

Answer 3

See, in place of x put theta/2

Answer 4

How would you go from there?

Answer 5

First form the equation in which in place of x there is theta/2

Answer 6

yeah i just did that.
Cos(theta/2)= 2cos^2(theta/2) - 1

Answer 7

No no in left hand side, its 2x so 2*(theta/2) = theta

Answer 8

so its theta=2cos^2(theta/2)-1

Answer 9

no its cos(theta)

Answer 10

cos(theta)=2cos^2(theta/2)-1
Like this?

Answer 11

Yes

Answer 12

Now, you have cos(theta) so evaluate cos(theta/2)

Answer 13

How would you do that?

Answer 14

See:

\[\large{\cos(\theta) = 2\cos^2(\theta/2) - 1}\]
\[\large{\implies 2cos^2(\theta/2) = cos(\theta)+1}\]
\[\large{\implies cos^2(\theta/2) = (cos(\theta)+1)/2}\]
\[\large{\implies cos(\theta/2) = \pm\sqrt{(cos(\theta)+1)/2}}\]

Answer 15

Now, you have cos(theta) , so calculate cos(theta/2).

Answer 16

I dont know how to evaluate.
I just started precalc and my teacher gave us a problem that would be on the test. if we get it we don't have to do it on the test.

Answer 17

Ok tell me can you add 1 to given value of cos(theta) ?

Answer 18

Cos(theta)+1?

Answer 19

Yes

what's the value of that ?

Answer 20

is it 0?

Answer 21

is the answer square root10 / 10