# Giving answers to the nearest degree, find in the interval 0<x<360

• Jun 20th 2011, 06:41 AM
neilofbodom
Giving answers to the nearest degree, find in the interval 0<x<360
Giving answers to the nearest degree, find in the interval 0<x<360 all the solutions of:

10 sin(x+26) cos(x+26)=1

rather than the answer, id like to know the solution ie how to work it out.

thanks,
neilofbodom
• Jun 20th 2011, 06:46 AM
Prove It
Re: Giving answers to the nearest degree, find in the interval 0<x<360
Use the identity $\displaystyle \displaystyle \sin{(2\theta)} \equiv 2\sin{(\theta)}\cos{(\theta)}$. If you let $\displaystyle \displaystyle x + 26 = \theta$ then

$\displaystyle \displaystyle 10\sin{(x + 26)}\cos{(x + 26)} \equiv 5\cdot 2\sin{(x + 26)}\cos{(x + 26)} \equiv 5 \sin{[2(x + 26)]}$.

So now you need to solve $\displaystyle \displaystyle 5\sin{[2(x + 26)]} = 1$.
• Jun 20th 2011, 06:49 AM
neilofbodom
Re: Giving answers to the nearest degree, find in the interval 0<x<360
oh ok. so then, ill find what x is and use the general solution of sin to find the other values, right?
• Jun 20th 2011, 07:00 AM
Prove It
Re: Giving answers to the nearest degree, find in the interval 0<x<360
Yes. Remember that the sine function is positive in the first and second quadrants.
• Jun 20th 2011, 07:10 AM
neilofbodom
Re: Giving answers to the nearest degree, find in the interval 0<x<360
ok thank you so much!