teach me the entire sin cos tan with right triangle and left triangle. And I'm in 6th grade so simplify it asmuch as u can. u asking why am I learning sin cos tan in 6th grade with age 12?? I not is cbse too. Its just coz I'm interested in higher class maths. Thanks if you answer. don't be greedy and answer something random I'll report ur answer
Answers
Step-by-step explanation:
Trigonometry was derived from the Greek words, 'Trigõnon' meaning 'Triangle' and 'Metron' meaning 'measure'.
Thus, the word itself gives out the whole study.
Now,
Trigonometry is the branch of mathematics dealing with the relations of the sides and angles of triangles and with the relevant functions of any angles.
It is a very big branch which contains a lot of formulas and equations.
Trigonometry at its base starts of with right triangles (Triangles having 1 angle equal to 90°), it later develops into relations of greater angles.
Trigonometry consists of 6 relationships between angles and its sides. They are:-
1. Sine (Sin)
2. Cosine (Cos)
3. Tangent (Tan)
4. Cosecant (Cosec)
5. Secant (Sec)
6. Cotangent (Cot)
Each of these functions link the angles to its sides.
To define these relations we firstly need a Triangle.
Let ΔABC be a right triangle, right angled at B, right angle is nothing but 90° angle.
(Refer image 1)
Next process is the choice of angle, each angle gives characters to each of its Corresponding sides.
Let's choose ∠A, then, AB is the adjacent side, BC will be the opposite side and AC will be the Hypotenuse.
(Refer image 2)
Let's say we chose ∠C, then, BC will be the adjacent side, AB will be the opposite side and AC will be the Hypotenuse.
(Refer image 3)
As you can see Hypotenuse never changes as Hypotenuse is the longest side of a triangle, and the longest side will always be opposite to 90° angle.
Now,
Just like in Algebra, we use x for the unknown value, in Trigonometry we use θ, and it's called 'theta'. Theta can be used to show any angle of any measure or degree.
Thus,
Sine function is the ratio of an angle's Opposite side to its Hypotenuse.
Sin θ = Opp./Hyp.
Cosine function is the ratio of an angle's Adjacent side to its Hypotenuse.
Cos θ = Adj./Hyp.
Tangent function is the ratio of an angle's Opposite side to its Adjacent side.
Tan θ = Opp./Adj.
Cosecant function is the ratio of an angle's Hypotenuse to its Opposite side.
Cosec θ = Hyp./Opp.
Secant function is the ratio of an angle's Hypotenuse to its Adjacent side.
Sec θ = Hyp./Adj.
Cotangent function is the ratio of an angle's Adjacent side to its Opposite side.
Cot θ = Adj./Opp.
Here, in our example
Sin A = BC/AC
Cos A = AB/AC
Tan A = BC/AB
Cosec A = AC/BC
Sec A = AC/AB
Cot A = AB/BC
Sin C = AB/AC
Cos C = BC/AC
Tan C = AB/BC
Cosec C = AC/AB
Sec C = AC/BC
Cot C = BC/AB
These are only basics, at first glance you might feel this is very difficult, but as time goes by you will realise that it is much simpler, since you are a 6th Grader it might be a bit difficult to understand but I believe that you are a bright student, so never worry alright?
At first you might think what of a use this is, but in future you will realise that Trigonometry is basically used in mostly all subjects and fields.
Hope it helped and believing you understood it........All the best
