Question

Write sin(x+1) in terms of unshifted sine and cosine. Write your answer using decimals.

Please provide explanation, I’m confused.

Answer 1

Answer: sin(x + 1) = 0.841*cos(x) + 0.540*sin(x)

Explanation:

Here we can use the relation:

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

In this case we have:

sin(x + 1)

This means that the graph of sin(x) is shifted one unit to the left.

But we can write this, using the above relation, as:

sin(x + 1) = sin(x)*cos(1) + sin(1)*cos(x)

Now we have no longer a shift, and we can replace:

sin(1) = 0.841

cos(1) = 0.540

Then:

sin(x + 1) = 0.841*cos(x) + 0.540*sin(x)