Basic Trigonometric Functions
Key Questions
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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:
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# Tanish J. · 3 · Nov 26 2014
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Have a look at this picture:
Hope it helps.
Gió
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Dec 26 2014
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These are all derived from the ratio's in a (right-angled) triangle.
If we divide the length of a side by the length of another side, we have a trigonometric function.
Lets take
#angle A# . Then there are six possible combinations for this division (#h# ,#a# and#b# are the sides)sine :
#sin A=a//h#
cosine :#cos A=b//h#
tangent :#tanA=a//b# These three are called the basic functions.
You will find them on most calculators.Note that:
#sinA/cosA=(a//h)/(b//h)=a/b=tanA# The other three are:
cosecant :#cscA=h//a=1/sinA# secant :
#secA=h//b=1/cosA# cotangent :
#ctgA=b//a=1/tanA# Normally these are not on a calculator, as they are easy to get from the other three.
(picture from Wikipedia) **
MeneerNask
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Jan 31 2015