Ensign

we know that maximum value of sinA=1,as sinA+7 =8,therefore sinA must be =1 hence
sinA=sin90( angle in degree) therefore as A=360n+((-1)^n)x90,where n belong to integers substituting n=0,1,2 we get A is less than 1000 and greater tha zero hence there are 3 solutions ALITER:sketch the graph of sinx & you will at 3 place sinx=1 for xis in 0 to 1000 degrees hence it has 3 solutions

sin a=8-7=1

a=90

a=90,360+90,720+90

Since $\sin\theta + 7 = 8$ , then $\sin\theta = 1$

We know that $\sin(90^{\circ}) = 1$ and $\sin(x + 2\pi) = \sin(x)$ .

So the solution set in the domain $[0^{\circ}, 1000^{\circ}]$ is $\{90^{\circ}, 450^{\circ}, 810^{\circ}\}$ .

Therefore there are $3$ solutions.