How Do I Establish a Transformation Identity?
y=M sin Bt + N cos Bt
y = sqrt( M^2 + N^2) sin (Bt+C)

C is any angle( in radians if t is real) having P=(M,N)on its terminal side [hint a first step is the following: M sin Bt + N cos BT = sqrt( M^2 + N^2)/sqrt( M^2 + N^2)*(M sin Bt + N cos Bt)

Question

How Do I Establish a Transformation Identity?
y=M sin Bt + N cos Bt
y = sqrt( M^2 + N^2) sin (Bt+C)

C is any angle( in radians if t is real) having P=(M,N)on its terminal side [hint a first step is the following: M sin Bt + N cos BT = sqrt( M^2 + N^2)/sqrt( M^2 + N^2)*(M sin Bt + N cos Bt)

campbell_st · Answer

for a sin x + b cos x can be written as rsin(x + c) 

$$r = \sqrt{a^2 + b^2}$$         tan c = b/a