how to simplify sin(x+3pi/2) using compound angle identity?

Answer 1

To simplify sin(x + (3π/2)) using compound angle identity, we can use the formula:

sin(a + b) = sin(a)cos(b) + cos(a)sin(b)

In this case, a = x and b = 3π/2. Substituting these values into the formula, we have:

sin(x + (3π/2)) = sin(x)cos(3π/2) + cos(x)sin(3π/2)

Now, let's evaluate the trigonometric functions involved:

cos(3π/2) = 0 (cosine of 3π/2 is 0)
sin(3π/2) = -1 (sine of 3π/2 is -1)

Substituting these values, we get:

sin(x + (3π/2)) = sin(x)(0) + cos(x)(-1)

Finally, this simplifies to:

sin(x + (3π/2)) = -cos(x)

So, using the compound angle identity, sin(x + (3π/2)) simplifies to -cos(x).