Question

If sine of the quantity x plus y end quantity equals radical 2 over 2 times sine of x plus radical 2 over 2 times cosine of x comma what is the value of y?

pi over 2
pi over 3
pi over 4
pi over 6

Answer 1

I think it’s pi over 4

Answer 2

Explanation:

The value of y is pi over 6. To solve for y, we use the fact that the sine of a sum is equal to the sum of the sines of each individual angle multiplied by the cosine of the other angle. This can be expressed mathematically as sin(x+y) = sin(x)cos(y) + cos(x)sin(y).

Substituting the given values into the equation, we have:

sin(x+y) = (√2/2)sin(x) + (√2/2)cos(x)

Rearranging, we can solve for y:

y = arcsin((√2/2)sin(x) + (√2/2)cos(x)) - x

Since x is equal to pi over 2, we can calculate y as follows:

y = arcsin((√2/2)sin(pi/2) + (√2/2)cos(pi/2)) - (pi/2)

= arcsin((√2/2)(1) + (√2/2)(0)) - (pi/2)

= arcsin(√2/2) - (pi/2)

= pi/6

Therefore, the value of y is pi over 6.