Sum and Difference Identities for Sine and Tangent

So now we want an identity for the sine of the sum of two angles. Let’s use some identities we already know to figure out this identity. First we’ll use a cofunction identity. distribute the negative and regroup (associative property) use cosine difference identity

Sum and Difference Identities for Sine Now we’ll use a cofunction identities again. Sum and Difference Identities for Sine

You will need to memorize these two as well You will need to memorize these two as well. Say them as you use them and you will get them memorized. Sum of angles for sine is, "Sine of the first, cosine of the second plus cosine of the first sine of the second." You can remember that difference is the same formula but with a negative sign.

A little harder because of radians but ask, "What angles on the unit circle can I add or subtract to get negative pi over 12?" hint: 12 is the common denominator between 3 and 4.

You will need to know these formulas so let's study them a minute to see the best way to memorize them. opposite cos has same trig functions in first term and in last term, but opposite signs between terms. same sin has opposite trig functions in each term but same signs between terms.

There are also sum and difference formulas for tangent that come from taking the formulas for sine and dividing them by formulas for cosine and simplifying (since tangent is sine over cosine).