Basic Trigonometric Functions
Key Questions
-
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
-
Have a look at this picture:
Hope it helps.
Gió
·
1
·
Dec 26 2014
-
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 andb 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
·
1
·
Jan 31 2015