SOLUTION: Rewrite &#8722;3sin(x)&#8722;1cos(x) as Asin(x+&#981;)? A: &#981;: When -pi < &#981; < pi

Algebra ->  Trigonometry-basics -> SOLUTION: Rewrite &#8722;3sin(x)&#8722;1cos(x) as Asin(x+&#981;)? A: &#981;: When -pi < &#981; < pi       Log On


   

Question 1040921: Rewrite −3sin(x)−1cos(x) as Asin(x+ϕ)?
A:
ϕ:
When
-pi < ϕ < pi
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
sin%28x%2By%29=sin%28x%29cos%28y%29%2Bcos%28x%29sin%28y%29
So then,
Asin%28x%29cos%28y%29=-3sin%28x%29
Acos%28y%29=-3
and
Acos%28x%29sin%28y%29=-1cos%28x%29
Asin%28y%29=-1
Then,
A%5E2%2Acos%5E2%28y%29%2BA%5E2%2Asin%5E2%28y%29=9%2B1
A%5E2=10
A=0+%2B-+sqrt%2810%29
and
tan%28y%29=%28Asin%28y%29%29%2F%28Acos%28y%29%29
tan%28y%29=-1%2F%28-3%29
y=0.322
So then,
-3sin%28x%29-cos%28x%29=-sqrt%2810%29%2Asin%28x%2B0.322%29
A=-sqrt%2810%29
phi=tan%5E%28-1%29%281%2F3%29