Question

How do you find the sin(theta/2) given that cos(theta)=3/5, 0 12 years ago

Answer 1

There's a so-called "half angle formula" for the sine; have you any familiarity with that?

Answer 2

I have the formula

Answer 3

Do i plug the cosine into the formula?

Answer 4

Please see http://www.sosmath.com/trig/douangl/douangl.html

From this reference I've gotten:
\[\cos ^{2}\frac{ a }{ 2 }=\frac{ 1 }{ 2 }(1+\cos a).\]

Answer 5

okay thanks

Answer 6

Hold...still working on this.

Answer 7

I should have given you the formula for the square of the SINE of (a/2). Sorry. But you can find that for yourself in the reference i've given you.

Now to apply it:

Answer 8

\[\sin ^{2}\frac{ \theta }{ 2 }=\frac{ 1 }{ 2 }(1-\cos \theta).\]
You've been told that cos theta=3/5, and that theta is in Quadrant 1.

Answer 9

Do the following:
(1) substitute 3/5 for cos theta in the formula I've just given you.
(2)Find the square root of both sides of this formula.

this will give you an expression for sin (theta/2). Choose the positive root, not the negative one.

Answer 10

Think: Why choose the positive root instead of the negative one?

Answer 11

Because the first quadrant is positive?

Answer 12

Yes, because the sine of theta/2 is the sine of a first-quadrant theta.
All set?

Answer 13

Yes. Thank you

Answer 14

You're welcome. Hope to work with you again! Best wishes. :)