find the exact value of the expression sin(105degrees)

Answer 1

sin(105 degrees) = sin(60 degrees + 45 degrees)

Using the sum-to-product formula for sine:
sin(a + b) = sin(a)cos(b) + cos(a)sin(b)

sin(105 degrees) = sin(60 degrees)cos(45 degrees) + cos(60 degrees)sin(45 degrees)

sin(105 degrees) = (√3/2)(√2/2) + (1/2)(√2/2)

sin(105 degrees) = (√6 + √2) / 4

Therefore, the exact value of sin(105 degrees) is (√6 + √2) / 4.