Trigonometry Part-2

Hello Friends, This is the Second Part of trigonometry So if you didn't checked Part-1 Than please check it first.Link is given in the end of this Article.

Friends Today we will learn few basic concepts of trigonometry.which are taught us by our teachers in Our School Time. Ok Let's see-

 In the above figure there you can see there are 4 quadrants

1st - (0°-90°)
2nd- (90°-180°)
3rd- (180°-270°)
4th- (270°- 360°)

• If the Value of θ lies between 0 to 90 than the element lies in 1st Quadrant and in first Quadrant every elements get converted in to a positive element.
• If the Value of θ lies between 90 to 180 than the element lies in 2nd Quadrant and in that Quadrant ,Only Sin and Cosec get converted in Positive Elements and rest are negative.
• If the Value of θ lies between 180 to 270 than the element lies in 3rd Quadrant and in that Quadrant ,Only Tan and Cot get converted in Positive Elements and rest are negative.
•  If the Value of θ lies between 270 to 360 than the element lies in 4th Quadrant and in that Quadrant ,Only Cos and Sec get converted in Positive Elements and rest are negative.

For More Clarification Check the Table given below:

(90-θ)	(90+θ)
Sin(90-θ)      = Cosθ	Sin(90+θ)      = Cosθ
Cos(90-θ)     = Sinθ	Cos(90+θ)     = -Sinθ
Tan(90-θ)     = Cotθ	Tan(90+θ)     = -Cotθ
Cot(90-θ)     = Tanθ	Cot(90+θ)     = -Tanθ
Sec(90-θ)     = Cosecθ	Sec(90+θ)     = -Cosecθ
Cosec(90-θ) = Secθ	Cosec(90+θ) = Secθ

{Note:- By this table make sure which element is converted in which element.because i didn't explained it before and nor i will do. Untill it is asked by anyone}
Few Important Notes

1. As you can see In case of 90-θ value will lie in 1st Quadrent So all the Elements are converted in a Possitive elements.And in case of 90+θ ,All Elements are in Second Quadrent So we just converted Sin and Cosec in the possitive elements and rests are negative.
2. And the other important point is that as you can see Sin get converted in Cos and Cos get converted in Sin and so on ,These elements are get converted only if it is -
   
   (90-θ) and (90+θ)
   Or
   (270-θ) and (270+θ)
   And in all other cases like (180-θ) and (180+θ) or (360-θ) and (360+θ) the elements remains same means Sin will be converted in Sin, it will not be converted in Cos.In that case you just have to check the Quadrant for the positive or negative Sign.

Important Formulas For Trigonometry

1.)Sin(A±B) = SinACosB±SinBCosA

2.)Cos(A±B) =CosACosB±SinACosB

3.)Tan(A±B)= TanA±TanB / 1± TanATanB

4.) Sin2A = 2SinACosA = 2TanA / 1+Tan^2A   (^2 means Square)

5.)Cos2A = 2Cot^2A-1 = 1-2Sin^2A = Cos^2A-Sin^2A = 1-Tan^2A / 1+Tan^2A

6.) Tan2A = 2TanA / 1-Tan^2A

Few more Basic and important Formulas if you Don't Know Just Check it

1.)Sin^2A+Cos^2A = 1

2.)Sec^2A-Tan^2A = 1

3.)Cosec^2A- Cot^2A =1

That's it friends i don't think you need to learn more formulas and if it will be needed i will explain it when we will start solving question's.

Don't miss the 3rd Part to learn how to apply these formulas and use of Quadrant properly.

And if you have any doubt regarding the material provided to you feel free to comment below.

Thank You☺