1. ## Compound Angle Formula

A question I have for my college maths assignment is ....

Show that sin(x+60)+sin(x+60)= sinx using the compound angle formula. Verify this by performing the calculations with the following angle, 0, 60 and 120.

[All numbers are degrees in the question.]

Working would be really appreciated and thank you in advanced.

Ben

2. Originally Posted by whitelockben
A question I have for my college maths assignment is ....

Show that sin(x+60)+sin(x+60)= sinx using the compound angle formula. Verify this by performing the calculations with the following angle, 0, 60 and 120.

[All numbers are degrees in the question.]

Working would be really appreciated and thank you in advanced.

Ben
$\displaystyle sin(x+60) + sin(x+60) = 2sin(x+60)$

$\displaystyle sin(A+B) = sinAcosB + cosAsinB$

A = x
B=60

$\displaystyle 2(sin(x)cos(60) + cos(x)sin(60)) = 2(\frac{sin(x)}{2} + \frac{\sqrt{3}}{2}cos(x) = sin(x)+\sqrt{3}cos(x)$

Sure you typed it correctly?

3. Sorry yes I did, its actually sin(x+60)+sin(x-60)=sinx .

4. Originally Posted by whitelockben
Sorry yes I did, its actually sin(x+60)+sin(x-60)=sinx .
In that case we have

$\displaystyle sin(A\pm B) = sinAcosB \pm cosAsinB$

From the unit circle: $\displaystyle cos(60) = \frac{1}{2}$ and $\displaystyle sin(60) = \frac{\sqrt3}{2}$

$\displaystyle sin(x)cos(60)+cos(x)sin(60) + [sin(x)cos(60) - cos(x)sin(60)]$$\displaystyle = 2sin(x)cos(60) = sin(x)$