1. ## 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 $7cos(x)-24sin(x)=Rcos(x+a)$

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

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

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

$25cos(x+73.74)=10$

$cos(x+73.74)=0.4$

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

$x=219.84, 352.68$

2. If you use Rsin(x-a) = R(sina*cosx - cosa*sinx)
then tan(a) = sin(a)/cos(a)
Find the value of a.
Substitute in the equation and find the value of x.