Expan each of the following using the compound-angle formulae:sin(x + 20degree)
sin(x+20) = sinx cos20 + cosx sin20
To expand the expression sin(x + 20°) using compound angle formulae, we can use the formula:
sin(A + B) = sin(A)cos(B) + cos(A)sin(B)
In this case, A = x and B = 20°, so we have:
sin(x + 20°) = sin(x)cos(20°) + cos(x)sin(20°)
To evaluate this expression, we need the values of sin(20°) and cos(20°). We can use a scientific calculator or reference table to find these values.
Assuming the values of sin(20°) and cos(20°) to be approximately 0.3420 and 0.9397 respectively, we can substitute these values into our formula:
sin(x + 20°) ≈ sin(x) * 0.9397 + cos(x) * 0.3420
So, the expanded form of sin(x + 20°) using compound angle formulae is sin(x) * 0.9397 + cos(x) * 0.3420.