CHAPTER II
SIX TRIGONOMETRIC FUNCTIONS
In mathematics, trigonometric functions are functions of angles. This lesson will describe the 6 main
trigonometric functions, use them to solve problems, and give some examples.
There are six main trigonometric functions:
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Sine (sin)
Cosine (cos)
Tangent (tan)
Secant (sec)
Cosecant (csc)
Cotangent (cot)
These functions are used to relate the angles of a triangle with the sides of that triangle. Trigonometric
functions are important when studying triangles and modeling periodic phenomena such as waves,
sound, and light.
Let’s define the sides of a triangle.
HYPOTENUSE
ADJACENT
OPPOSITE
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The hypotenuse is the side opposite the right angle. The hypotenuse is always the longest side
of a right triangle.
The opposite side is the side opposite to the angle we are interested in, theta.
The adjacent side is the side having both the angles of interests (angle theta and the right angle)
The relationship between the trigonometric functions and the sides of the triangle are as follows:
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Sine (theta) = opposite / hypotenuse
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Cosecant (theta) = hypotenuse / opposite
Cosine (theta) = adjacent / hypotenuse
Secant (theta) = hypotenuse / adjacent
Tangent (theta) = opposite / adjacent
Cotangent (theta) = adjacent / opposite
Note: A good way to remember the definitions of sine, cosine, secant, and tangent is with the memory
of socahtoa. The other three functions- cosecant, secant, cotangent- are just reciprocals of the first
three.
We could make use of a scientific calculator to obtain the trigonometric value of an angle.
Example: Find the value of cos 6.35˚.
Solution:
Press COS 6.35 DEG
=
cos 6.35˚ = 0.9939 (correct to 4 decimal places)
Example:
Find the value of sin 40˚ 32 ’ .
Solution:
Press SIN 40 DEG 32
=
sin 40˚32 ’ = 0.6499 (correct to 4 decimal places)