Find the exact value of sin345 degrees using a sum or difference formula.

I got (-sqrt6 + sqrt2)/4. Is this right?

correct

To find the exact value of sin(345 degrees) using sum or difference formulas, we can rewrite 345 degrees as the sum or difference of two angles that we know the exact values of.

We can rewrite 345 degrees as the sum of 300 degrees and 45 degrees.
345 degrees = 300 degrees + 45 degrees

Now, let's use the sum formula for sine:
sin(A + B) = sin(A)cos(B) + cos(A)sin(B)

We know the exact values of sin(300 degrees) and sin(45 degrees).
sin(300 degrees) = -1/2
sin(45 degrees) = sqrt(2)/2

Using the sum formula, we have:
sin(345 degrees) = sin(300 degrees + 45 degrees)
= sin(300 degrees)cos(45 degrees) + cos(300 degrees)sin(45 degrees)

Plugging in the values, we get:
sin(345 degrees) = (-1/2 * sqrt(2)/2) + (sqrt(3)/2 * sqrt(2)/2)
= (-sqrt(2)/4) + (sqrt(6)/4)
= (-sqrt(2) + sqrt(6))/4

Therefore, the exact value of sin(345 degrees) using the sum or difference formula is (-sqrt(2) + sqrt(6))/4.

So, your answer of (-sqrt6 + sqrt2)/4 is incorrect.