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TRIGONOMETRY

                      💁  TRIGONOMETRY   🙋


INTRODUCTION:-The word trigonometry is derived from three Greek words 'Tri'( means three)  'gon' (means sides) and  'metron ' (means measure) i.e measurement of sides & angles of triangle .
DEFINITION:-Trigonometry is a branch of mathematics which deals with measurement of angles and sides of triangle . 



TRIGONOMETRIC RATIO:-  Ratio of the sides of a right triangle with respect to its acute angles is called trigonometry ratio of the angles. 

       STANDARD TRIGONOMETRY RATIO( T - RATIO). 
1. Sin A =   P                             4. Cosec A =  H   
                   H.                                                   P

2. Cos A  =    B                           5. Sec A =      H   
                      H.                                                 B.

3. Tan A  =   P                           6. Cot A  =      B  
                     B                                                   P.                                             
                                                                                                         
 ✅  NOTE ;- The  standard T-ratios of angle  i.e sine (abbreviated as sin),  Cosine is written as cos , tangent is written as tan, Cosecant is written as Cosec, Secant is written as Sec, Cotangent is written as Cot.
✅1. PERPENDICULAR= P.        2. BASE = B .              3. HYPOTENUSE= H.

                                    IMPORTANT QUESTION
 Q1. If cos A  = 9/41. Find  the  other  trigonometric  ratios  of A. using  Pythagoras’ theorem.

 Q2. In   a  ∆ABC ,  Right angled  at B , It  is given that   AB =12 CM  and BC= 5 CM. find th Value  of  1. SinA   2. SinC   3.CosA     4. CosC   5.TanA  6.TanB.

Q3. In a  ∆ABC ,Right angled  at B , It  is given that  AB  =7 CM and (AC—BC) = 1CM.Find the value OF  1. SinA   2. SinC    3.CosA   4. CosC   5.TanA   6.TanC

 Q4. In a ∆ABC, Right angled at B It is given thatAB  = 5 CM and  BC +AC = 25 CM Find the values of  1. SinA   2 CosA    5.TanA     6.TanC  .                            
Q5.In a triangle ABC, right angled at B, in which AB= a and BC=a.
 Find the value of SecA .

Q6.. CosA = 5/13 Find the value of    SinA --  CotA.     [B]        CotA  +       1             

                                                                2 TanA                                       CosA.

Q7. If SinA  + CosecA  = 2. Find  the  value  of  sin2A +  Cosec2A .

Q8. If 4 Sinθ  = 3 cosθ .  find the value of  {a} sinθ . {b}Cosθ.      {c} tanθ .

Q9. In a ∆ABC , Right angled  at B , It  is given that  AB  = 5 CM          and  BC + AC  = 25 CM  Find the value 1.SinA 2.SinC  3.CosA          4. CosC  5.TanA  6.TanC 

10. Express the trigonometric ratios  sinA   ,CosA   , secA    and     tanA    In  terms of  cotA.

Q11. Prove the following identities:-   

 

a. ( Cosecθ – cotθ)2   =     1—cosθ

                                               1+ cosθ                          

   b  Tan480   × Tan23o   ×Tan42 o     × Tan67o  =  1.

Q12. Evaluate :---

             COS 45o 

     Sec 30o + Cosec30o              

Q13. If  Sinθ + sin2θ = 1. prove that  cos2θ  + cos4θ = 1.

Q14.   Cos θ    +   1+ sin θ     =2 SEC θ  Prove the following identities

          1+ Sinθ        cos θ

Q15.If Sin 3A = COS( A- 10O) , Where 3A is an acute angle then, find the value of angle A.

Q13.Cos1o x Cos2o x Cos3o x Cos4o  x Cos5o  xCos6o ......xCos90o  find the value=?

Q14.In a right triangle ABC at B=90°, AB= 24CM and  BC= 7 cm . determine the sinA    SinC     CosA     CosC     TanA     TanC     CotA      CotC      CosecA  

 

Q15. If Tan (A+B) = √3 and  Tan( A-- B)= 1/√3   A˃B , 0O ˃ A+B,< 90O   Find the A &B.

ANSWER

                
 

     Q1. SECA= √2.       

      Q2.  A]    395/3744.           [B.] 181/60.

                                            

Q3.   sin2A +  Cosec2A = 2.

Q4.  {a}    sinθ .= 3/5       {b}  Cosθ. =4/5     {c} tanθ .= 3/4    

Q5. 1. SinA    2. SinC     3.CosA     4. CosC     5.TanA     6.TanC 

Q6.  1. SinA   2. SinC    3.CosA     4. CosC    5.TanA     6.TanB

Q7.  sinA   ,CosA   , secA    and     tanA  

Q9                                3√2  -  √6

                                                                 -----------------------------------------

                                                          8.         

        Q12.          25    DEGREE 

 Q13.      0 DEGREE 

Q14.sinA =7/25   SinC =24/25    CosA =24/25    CosC =7/25    TanA  =7/24   TanC=24/7           CotA  = 24/7    CotC=7/24      CosecA  =25/7

Q15. A= 45 DEGREE   B= 15 DEGREE


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