trouble reading sin graph, not accurate anymore?

my problem is that though I am aware i can use Rsin(x-a) to express this equation **i never get the same answers as the book which uses Rcos(x+a).** The book chose to express the equation as Rcos(x+a), however i want to express it as Rsin(x-a) because i am unable to read off the sin graph, it does not work anymore the reading are inaccurate.** Can someone represent the equation as Rsin(x-a) and tell me how they got there?**

__the books R(cos.. working__

the equation$\displaystyle 7cos(x)-24sin(x)=Rcos(x+a)$

$\displaystyle R=sqrt(7^2+24^2)=25$

$\displaystyle cos a=(7/25)or sin a=(24/25)$ this results in a=73.74

$\displaystyle 7cos(x)-24sin(x)=10$

$\displaystyle 25cos(x+73.74)=10$

$\displaystyle cos(x+73.74)=0.4$

$\displaystyle x+73.74=66.42, 360+/-66.42$

$\displaystyle x=219.84, 352.68$