Sum Or Difference Of Two Angles Formula Sheet
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6Section 8.4 – Sum and Difference Formulas
In this section we will learn formulas for trig functions that involve the sum or difference of two angles. Let's start with
the sum and difference formulas for cosine and sine:
To help you remember these formulas, let's think of them this way:
To expand a sum/difference within cosine: (multiply cosines together) {opposite sign} (multiply sines together)
*Just remember "CGO": For Cosine, Group like functions and use the Opposite sign*
To expand a sum/difference within sine: (multiply sine by cosine) {same sign} (multiply cosine by sine)
*Remember "SMS": For Sine, Mix the functions and use the Same sign*
*In both cases, the first trig function after the equals sign is the same as the original trig function.*
YOU NEED TO MEMORIZE THESE FORMULAS!!!
cos(45
30 )
For example, let's expand
. We remember that for cosine, we are going to multiply together like
functions and put the opposite sign between them. So since the original problem has a minus sign, we'll use a plus sign
in our expansion. Thus:
cos(45
30 ) cos _____ cos _____
sin_____ sin_____
___
___ +
___
___
cos(45
30 )
Since the original problem was
, this could have been stated as "Find the exact value of cos(15)."
Let's look at another example where the problem is originally stated in this manner: Find the exact value of sin(120).
For Sines, remember that we Mix sines and cosines, starting with sine of the first angle, and we use the Same sign. We
need to decide which two of our commonly-used angles (30, 45, and 60) add or subtract to equal 120.
sin(120 ) sin(____ + ____ )
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