no idea how to do this double angle formulae question

Here is the question:

Given that pi < theta < 3pi/2, find the value of sintheta/2, when costheta = 24/25

:smile:

Try drawing a triangle, 25 is the hypotenuse, 24 is the adjacent side to the angle. Work out the length of the opposite side.

Then see if you can find sin theta after that.

(edited 7 months ago)

Reply 2

adxmmm

Original post by Okayn

Try drawing a triangle, 25 is the hypotenuse, 24 is the adjacent side to the angle. Work out the length of the opposite side.

Then see if you can find sin theta after that.

Thanks now i've got that sin theta = 7/25 but how do I get that as sin theta/2? :smile:

Reply 3

Okayn

Is just the theta over 2 or is the whole thing (sin theta) over 2.

Reply 4

adxmmm

Original post by Okayn

Is just the theta over 2 or is the whole thing (sin theta) over 2.

Only the theta is over 2

Reply 5

mqb2766

Original post by adxmmm

Only the theta is over 2

You should know the double or half angle identities so
cos(2A) = 1 - 2sin^2(A)
and rearranging gives the 1/2 angle identity
sin(A) = +/-sqrt((1-cos(2A)) / 2)
so just replace A with theta/2. Then adjust the sign for the stated domain.

However ... if pi<theta<3pi/2, youd expect cos(theta) to be negative, so is your question/OP correct?

(edited 7 months ago)

Reply 6

adxmmm

Yes here is the question. However, i get the same answer as the answer sheet when I use cosa as a positive number.

Reply 7

mqb2766

Original post by adxmmm

Yes here is the question. However, i get the same answer as the answer sheet when I use cosa as a positive number.

What did the answer sheet say / your working? If theta is in that range, cos must be negative.

(edited 7 months ago)

Reply 8

adxmmm

Original post by mqb2766

What did the answer sheet say / your working? If theta is in that range, cos must be negative.

The answer is sqrt(2) / 10

Reply 9

mqb2766

Original post by adxmmm

The answer is sqrt(2) / 10

Something screwy with the question/answer then, as for
pi < theta < 3pi/2
pi/2 < theta/2 < 3pi/4
neither cos(theta)=24/25 nor sin(theta/2) = sqrt(2)/10 satisfy those ranges. However, for the acute angle theta, then cos(theta)=24/25 and sin(theta/2) is sqrt(2)/10.