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Trig Formulas
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This is not a complete list of trig formulas. This is just a list of formulas that I’ve
found to be the most useful in a Calculus class. For a complete listing of trig formulas you
can download my Trig Cheat Sheet.
Complete the following formulas.
1. 
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Note that this is true for ANY
argument as long as it is the same in both the sine and the cosine. So, for example :
2.
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If you know the formula from Problem 1 in this section you can get
this one for free.
Can you come up with a similar
formula relating and ?
3.
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This formula is often used in
reverse so that a product of a sine and cosine (with the same argument of
course) can be written as a single sine.
For example,
You will find that using this
formula in reverse can significantly reduce the complexity of some of the
problems that you’ll face in a Calculus class.
4. (Three possible formulas)
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5. (In terms of cosine to the first power)
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This is really the second formula
from Problem 4 in this section rearranged and is VERY useful for
eliminating even powers of cosines. For
example,
Note that you probably saw this
formula written as
in a trig class and called a
half-angle formula.
6. (In terms of cosine to the first power)
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As with the previous problem this
is really the third formula from Problem 4 in this section rearranged and is
very useful for eliminating even powers of sine. For example,
As shown in this example you may
have to use both formulas and more than once if the power is larger than 2 and
the answer will often have multiple cosines with different arguments.
Again, in a trig class this was
probably called half-angle formula and written as,