A quick reference guide for solving trigonometric proofs and some basic trig identities to use.
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Method 1
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Pick one side of the equation (usually the most complicated side) and work with that side until it is equal to the other side
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Method 2
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Work with both sides simultaneously until they are both equal to the same expression.
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Rewrite
Rewrite the expression in terms of sine and cosine only
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Multiply by One
Multiply the numerator and denominator of a rational expression by a carefully chosen "one"
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Combine fractions
Write sums and differences of rational expressions as a single fraction
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Factor
Factor trigonometric expressions, using "u-substitution" as needed
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Pythagorean Theorem
Look for combinations or portions of Pythagorean Identities. Remember that you can multiply, divide, add or subtract the identity to get a new version.
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Goal
Always keep the goal in mind. As you manipulate one side of the equation, keep the other side in mind. Look for commonalities
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sin (-x) = -sin (x)
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tan (x) = sin (x) / cos (x)
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csc (x) = 1/sin (x)
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cos (-x) = cos (x)
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cot (x) = cos (x) / sin (x)
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sec (x) = 1/cos (x)
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tan (-x) = -tan (x)
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cot (x) = 1/tan (x)
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sin (pi/2 - x) = cos (x)
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cos (pi/2 - x) = sin (x)
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tan (pi/2 - x) = cot (x)
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sin (a +/- b) =
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sin (a) cos (b) +/- cos (a) sin (b)
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cos (a +/- b) =
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cos (a) cos (b) -/+ sin (a) sin (b)
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sin (2x)
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cos (2x)
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2 sin (x) cos (x)
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cos2 (x) - sin2 (x)
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1 - 2 sin2 (x)
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2 cos2 (x) - 1
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Cheatography n. The art of mapping complex subjects into clear, instantly navigable reference guides.
