How are the 6 basic trigonometric functions related to right triangles?

1 Answer
Nov 26, 2014

The six basic trigonometric functions are:
1. Sine, #sintheta#
2. Cosine, #costheta#
3. Tangent, #tantheta#
4. Cotangent, #cottheta#
5. Secant, #sectheta#
6. Cosecant, #csctheta#

Take the following triangle for example:

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Let the angle marked at A be #theta#.
The longest side of the triangle is the hypotenuse, the side next to the angle is the adjacent and the side opposite to it is the opposite.

Then,

#sintheta =(opp)/( hyp)=a/h#

#costheta =(adj)/( hyp)=b/h#

#tantheta =(opp)/(adj)=a/b=(sintheta)/(costheta)#

#cottheta =(adj)/(opp)=b/a=(costheta)/(sintheta)=1/tantheta#

#sectheta =(hyp)/(adj)=h/b=1/costheta#

#csctheta =(hyp)/(opp)=h/a=1/sintheta#

Now if we the triangle were to have sides 3, 4 and 5 units long such that
#a=4, b=3, h=5#
The six basic trigonometric functions would be:

#sintheta =a/h=4/5#

#costheta=b/h=3/5#

#tantheta =a/b=4/3#

#cottheta =b/a=3/4#

#sectheta =h/b=5/3#

#csctheta =h/a=5/4#