From Wikipedia, the free encyclopedia Mnemonics in trigonometry
Mnemonics in trigonometry
In trigonometry, it is common to use mnemonics to help {1 \over \tan A} = \cot A & \text{or} & {1 \over
remember trigonometric identities and the relationships \cot A} = \tan A \\ \\ {1 \over \sec A} = \cos A &
between the various trigonometric functions. For exam- \text{or} & {1 \over \cos A} = \sec A \end{array}
ple, the sine, cosine, and tangent ratios in a right triangle
can be remembered by representing them as strings of
letters, for instance SOH-CAH-TOA in English: Reading down any triangle gives the standard identities
Sine = Opposite ÷ Hypotenuse (starting at the top and going clockwise):
Cosine = Adjacent ÷ Hypotenuse
Tangent = Opposite ÷ Adjacent
One way to remember the letters is to sound them out
phonetically (i.e. "SOH-CAH-TO-A").[1] Another method
S
is to expand the letters into a sentence, such as "Some Reading a function and dividing the two consecutive
Old Hippy Caught Another Hippy Trippin’ On Acid".[2] clockwise or counter clockwise neighbors gives these
identities:
Mnemonic chart (Starting at tan and going clockwise)
Another mnemonic permits all of the basic identities to
be read off quickly. Although the word part of the
mnemonic used to build the chart does not hold in Eng-
lish, the chart itself is fairly easy to reconstruct with a lit-
tle thought. (Functions appear on the left, co-functions
on the right, a 1 goes in the middle, triangles point down,
and the entire drawing looks like a radiation symbol.)
(Starting at tan and going counter-clockwise)
Trigonometric identities mnemonic
Reading across the central 1 in any direction gives
reciprocal identities:
Failed to parse (PNG conversion failed; check for
correct installation of latex and dvipng (or dvips +
gs + convert)): \begin{array}{} {1 \over \sin A} =
\csc A & \text{or} & {1 \over \csc A} = \sin A \\ \\
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From Wikipedia, the free encyclopedia Mnemonics in trigonometry
References
[1] Weisstein, Eric W., "SOHCAHTOA" from
Reading a function and multiplying the two nearest MathWorld.
neighbors gives these identities (starting at tan and going [2] A sentence that is more appropriate for high school
clockwise): is, "Some old horse came a’hopping through our
alley." Foster, Jonathan K. (2008). Memory: A Very
Short Introduction. Oxford. p. 128. ISBN 0192806750.
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Categories:
• Trigonometry
• Mnemonics
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