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cos(A − B) = cos A cos B + sin A sin B. (8) Notice that by remembering the identities (2) and (3) you can easily work out the signs in these last two identities.

Positive: sin, csc Negative: cos, tan, The Unit Circle sec, cot 2Tt 900 Tt 3Tt 2 2700 Positive: sin, cos, tan, sec, csc, cot Negative: none 600 450 300 2 2 1500 1800 21 (-43, 1200 1350 2Tt …

This is very useful information about the function sin(x) but it doesn’t tell the whole story. For example, it’s hard to tell from the formula that sin(x) is periodic.

d (cos x + dx i sin x) = sin x + i cos x = i(cos x + i sin x) so cos x + i sin x has the correct derivative to be the desired extension of the exponential function to the case c = i.

The first digit of a SIN indicates province of registration.

2 sin x 2 Exercise 1: By taking the real part in (2) find a formula for cos x + cos 2x + · · · + cos nx. Exercise 2: Use sin(a + x) + sin(a + 2x) + · · · · · · + einx)} to compute a formula for sin(a + x) + …