given the funtion y= A sen x + B cos x which of the next conditions must have the coeficients A and B.....?

Question

... so y= sqr (2) when x= (3 * 3.14) / 4

help me please!!!

the answers are :

a) A + B =2

b) A - B = 2

c) A - B = sqr (2)

d) B - A = 2

which one is correct??

yes I meant sin...

what happens is that I am from a latin country, and here is sen... it is actually seno... so I didn't know it was different in English SORRY

Answer 1

y = A sin x + B cos x

According to the given information:
sqrt(2) = A sin(3 pi / 4 ) + B cos(3 pi / 4)

sin(3 pi / 4) = sqrt(2)/2 and cos(3 pi / 4) = -sqrt(2)/2, so we get:
sqrt(2) = A ( sqrt(2) / 2 ) + B ( -sqrt(2) / 2 )

Factor out sqrt(2)/2 and get:
sqrt(2) = ( sqrt(2) / 2 ) ( A - B )

In order for the right side to equal the left side, A - B must be 2:
sqrt(2) = ( sqrt(2) / 2 ) ( 2 )

So the correct answer is b) A - B = 2

Answer 2

Note sin (3pi/4) = sqrt(2)/2, cos (3pi/4) = - sqrt(2)/2. So for

A = 1 and B = -1, the sum is sqrt(2). Correct Answer

A - B = 2

Bozo

Answer 3

I assume you mean

y = Asin x + Bcos x

In that case

sin(3π/4) = 1/√2
cos(3π/4) = -1/√2

y = Asin x + Bcos x = Asin(3π/4) + Bcos(3π/4)
y = A/√2 - B/√2 = √2
A - B = (√2)² = 2

The answer is B.

Answer 4

What is "sen"?