To solve a problem like the one above, you need
Hypotenuse
to memorize the relations between the sides and
Opposite
the angles of a right triangle. A convenient
mnemonic2 for doing so is “SOHCAHTOA”
θ
pronounced as a single word.
Adjacent
Referring to the diagram above right:
Opposite
SOH reminds us that: sinθ =
(1-3)
Hypotenuse
Adjacent
CAH reminds us that: cosθ =
(1-4)
Hypotenuse
Opposite
TOA reminds us that: tanθ =
(1-5)
Adjacent
Points to remember:
1. The angle θ is never the 90 degree angle.
2. The words “opposite” and “adjacent” designate sides relative to the angle. For instance,
the cosine of θ is the length of the side adjacent to θ divided by the length of the
hypotenuse.
You also need to know about the arcsine and the arccosine functions to solve the example
problem above. The arcsine function is the inverse of the sine function. The answer to the
question, “What is the arcsine of 0.44?” is, “that angle whose sine is 0.44 .” There is an arcsine
button on your calculator. It is typically labeled sin-1, to be read, “arcsine.” To use it you
probably have to hit the inverse button or the second function button on your calculator first.
The inverse function of a function undoes what the function does. Thus:
−
sin 1 sinθ = θ
(1-6)
Furthermore, the sine function is the inverse function to the arcsine function and the cosine
function is the inverse function to the arccosine function. For the former, this means that:
sin(
−1
sin
x) = x
(1-7)
2 A mnemonic is something easy to remember that helps you remember something that is harder to remember.
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