Sum Or Difference Of Two Angles Formula Sheet Page 2
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6Now let's look at a couple examples of angles in radians. A good rule of thumb is that if the denominator is 12, then it is
a combination of
and either
or
, since the least common denominator of 4 and 3 (and also 4 and 6) is 12.
4
3
6
For help with these problems, remember that:
,
, and
.
4
12
3
12
6
12
Example: Find the exact value of each expression. Remember CGO and SMS!
5
cos
cos
a)
12
sin
b)
12
We can also do these problems in reverse, where we start with an expansion and condense it into a single sine or cosine
function. Again, it is helpful to remember CGO and SMS (if like functions are Grouped together, it is an expansion of a
Cosine function, and if the functions are Mixed together, then it is an expansion of a Sine function).
Example: Find the exact value of each expression.
sin20 cos80
cos20 sin80
a)
Because the sines and cosines are Mixed together, we know this is the expansion of a __________ function.
Completing the final letter of our "SMS" guide, we know that the condensed function will use the __________
sign as the expanded one, so the condensed function will be: _______________________________________
Now find the exact value of this trig function.
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