Trigonometry Mizo tawnga Hrilhfiahna leh Competitive exam na a pawimawh thin te. By : Elisa Hauheng

                      

                             TOPIC : TRIGONOMETRY 

Q.Eng nge trigonometry chu? 

Ans:  Trigonometry han tih hian thil eng emaw deuh ani hran lova mathematics peng zinga Pakhat tangkai em em mai ani.He trigonometry hi hi Right angle Triangle 📐 a size angle te zirna leh thildang ah pawh tangkai na leh pawimawh na a ngah hle bawk.

Note: Kum 6th century B.C.  kal ta ah khan Greek philosopher mathematician bawn em em mai Pythogoras a chuan Right angle triangle hmang hian formula tangkai leh tha em em mai tun thlenga kan la hman hi a hmu chhuak hlauh mai a, a hming chawi hian chu formula chu Pythogoras Theorem tih ani.

Term pawimawh em em mai te: 

1.Hypotenuse: Right angle triangle 📐 a a line sei ber kha ani.H or h ti te pawh in kan ziak thin.

2.Base : A hming dang chu adjacent tih ani a, kan triangle 📐 in nghah na kha ani mai a perpendicular leh hypotenuse nilo line kha ani mai.A tlangpui in B or b in kan ziak thin 

3.Perpendicular: Hei hi a hming dang chu Opposite angle tih ani a, a awmzia chu hypotenuse ep chiah a mi line kha ani a base atang a teh in a base nen a an inkar angle hi 90° ani ngei ngei tur ani.A tlangpui in P or p in kan ziak thin.

                                                                                  

📍Pythagorean theorem Hrilhfiahna:  Pythogoras Theorem in a a sawi chu Right angle triangle lo nei ta ila hypotenuse square hian base leh Perpendicular square belh a tluk tih na ani he tiang hian.

                         p² + b² = h²

[Note:  Hethil hi a pawimawh em em a height and Distance zawn na kawng ah phei chuan nasa takin min pui thei dawn ani.]

Trigonometric Identities hrang hrang te:

 Heng hi hriat chian hle tur ani.

  ||        Hriat tur pawimawh em em mai

    Lhs= Rhs( left and right hand side tihna)

[.Note ; "=" Sign a awm reng reng hian Lhs ami eng number or number ni kher lo (variables) pawh nise Rhs or equal to leh lama kan sawn dawn in a sign an thlak thin hetiang hian.

                    '+' Chu '-'  ah .

                  '-'  anih chuan '+' ah ] ||

📄📍Trigonometric Identities hrang hrang te:

 Heng hi hriat chian hle tur ani.

1). sin²a + cos²a= 1 or

 sin²a= 1-cos²a.

 Or cos²a= 1-sin²a

2). 1+tan²a = Sec²a

Or tan²a= Sec²a - 1

Or sec²a - tan²a= 1

3).1 + cot²a = cosec²a

Or cot²a= cosec²a - 1

Or cosec²a - cot²a = 1

🖍️📍Quadrants :- Graph plane a X-axis leh Y-axis te hi limun 4-ah a then theih a chungte chu quadrant tih a ni.

                                         |.    

           2nd Quadrants    |          1st Quadrant             

              Quadrant           |.       4 Quadrant 

                         3rd          |

                        Fig: Cartesian plane X and Y

Hriat tur te:

1 st Quadrants: tah hi chuan x leh y hi Positive (+) ani ve ve dawn.

2nd Quadrants: tah hi chuan x hi (-) negative y hi (+) positive ve thung

3rd Quadrants: tah hi chuan x leh y hi (-) negative ve ve thung ani.

4 th Quadrant:  tah hi chuan x hi (+) positive y ve thung hi (-) negative ani thung.

Note:  

1.Any point on the x axis is represented as (x,0)

2.Any point on the y axis is represented as (0,y)

3.Any point on the x and y axis is represented as (x,y).

MPSC Practice Questions:

Q1.Any point on the x-axis is of the form[Civil service paper- 2016]

a) (x,x)

b) (x,0)

c) (x,y)

d) (0,y)

Ans: Any point on the x axis is represented as (x,0)

Q2. (-2,3) lies in the [ ASI 18-Home]

a) I quadrant

b) II quadrant

c) III quadrant

d) IV Quadrant 

Ans: Quadrants II.

A chhunzawmna hi ka hman hun ah ka lo dah leh ang...