# Quick Question (Double Angle Formula)

• Dec 10th 2007, 06:50 PM
Hasan1
Quick Question (Double Angle Formula)
The question says find the exact value of:

sin 67.5

This is a double angle identity question and I think im getting confused because its actually a half angle (135/2).

I have to use sin(2A) = 2sin(A)cos(A)

(I know there is a half angle formula, but our teacher never taught us that and he said we should be able to do it with the sine double angle formula anyway)
• Dec 10th 2007, 06:54 PM
Jhevon
Quote:

Originally Posted by Hasan1
The question says find the exact value of:

sin 67.5

This is a double angle identity question and I think im getting confused because its actually a half angle (135/2).

I have to use sin(2A) = 2sin(A)cos(A)

(I know there is a half angle formula, but our teacher never taught us that and he said we should be able to do it with the sine double angle formula anyway)

on the contrary, this is more easily done as a half angle problem: $\displaystyle \sin 67.5 = \sin \frac 12(135)$
• Dec 10th 2007, 06:58 PM
Hasan1
yeh but our teacher never gave us the half angle formula in class so we have to use the double angle formula to solve this question
• Dec 10th 2007, 07:15 PM
Jhevon
Quote:

Originally Posted by Hasan1
yeh but our teacher never gave us the half angle formula in class so we have to use the double angle formula to solve this question

trust me, the double angle formula is way more trouble than it's worth here. i thin it's far more likely that your professor expects you to study ahead rather than apply the double angle formula.

note that $\displaystyle \sin \frac x2 = \pm \sqrt{\frac {1 - \cos x}2}$

now you have to know what quadrant the original angle is in in order to know if it should be a plus or minus
• Dec 11th 2007, 04:26 PM
Hasan1
okay I'll ask him thanks for the help:cool: