This is a free lesson from our course in Trigonometry
In this lesson, you'll learn how to relate the angles and sides of a right triangle. It is followed by explanation of the
trigonometric functions. This is done with the help of several
examples, video and explanation by instructor in own hand writing. It includes the
practice questions with solutions to help solving math problems.
In a right angle triangle, for angle
, the name of the sides
is:
(Continued from above) The trigonometric ratios sine
, cosine
, and tangent q (in
short form sin
, cos
, and tan
) are defined as:
sin
= opposite/hypotenuse
cos
= adjacent/hypotenuse
tan
= opposite/adjacent
To help you remember the important facts, you can use SOH CAH TOA.
SOH stands for Sine equals Opposite over Hypotenuse i.e.,
sin
= opposite/hypotenuse,
CAH stands for Cosine equals Adjacent over Hypotenuse i.e.,
cos
= adjacent/hypotenuse
TOA stands for Tangent equals Opposite over Adjacent i.e.,
tan
= opposite/adjacent,
where
represents an angle.
Trigonometric functions are defined as ratios of the sides of a right triangle (sine,
cosine, tangent, cotangent, secant, and co secant), and can equivalently be defined
as the lengths of various line segments from a unit circle. More modern definitions
express them as infinite series or as solutions of certain differential equations,
allowing their extension to arbitrary positive and negative values and even to complex
numbers.
The reciprocal functions of sine, cosine and tangent are cosecant,
secant and cotangent respectively. They are generally written as csc, sec and cot.
For any angle
, these
functions can be expressed as
csc
= 1/sin
sec
= 1/cos
cot
= 1/tan
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