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TRIGONOMETRY PART 2


Q1. In a triangle ABC, right angled at B, in which AB = a and BC = a .Find the value of SecA .

Q2. CosA = 5/13 Find the value of    SinA --  CotA.     [B]        CotA  +       1             

                                                                2 TanA                                       CosA.

Q3. If  SinA  +  CosecA  = 2 ,  Find  the  value  of  sin2A +  Cosec2A .

Q4. If 4 Sinθ  = 3 cosθ .  find the value of  {a}    sinθ .       {b}  Cosθ.      {c} tanθ .

Q5. In a ∆ABC , Right angled  at B , It  is given that  AB  = 5 CM and  BC + AC  = 25 CM 

   Find the values of 1. SinA    2. SinC     3.CosA     4. CosC     5.TanA     6.TanC 

Q6. 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.TanB

Q7. Express the trigonometric ratios  sinA   ,CosA   , secA    and     tanA    In  terms of  cotA.

Q8. Prove the following identities:-   

 

a. ( Cosecθ – cotθ)2   =     1—cosθ

                           1+ cosθ                          

   b  Tan480  Tan23o  Tan42o   Tan67o  = 1.

Q9. Evaluate :---

             COS 45o 

     Sec 30o + Cosec30o              

Q10. If  Sinθ + sin2θ = 1. prove that  cos2θ  + cos4θ = 1.

Q11.   Cos θ    +   1+ sin θ     =2 SEC θ  Prove the following identities

       1+ Sinθ        cos θ

Q12.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  x  Cos6o …………………Cos90o . 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.

type 02

 


 

 





Q1. A tower stands vertically on the ground. From a point on the ground,which is 15 m away from the foot of the tower, the angle of elevation of the top of the tower is found to be 60°. Find the height of the tower.

Q2. An observer 1.5 m tall is 28.5 m away from a chimney. The angle of elevation of the top of the chimney from her eyes is 45°. What is the height of the chimney?

Q3 : The shadow of a tower standing on a level ground is found to be 40 m longer when the Sun’s altitude is 30° than when it is 60°. Find the height of the tower.

 

Q4 . A tree breaks due to storm and the broken part bends so that the top of the tree touches the ground making an angle 30° with it. The distance between  the foot of the tree to the point where the top  touches the ground is 8 m.  Find the height of the tree

 

Q5. The angle of elevation of the top of a tower from a point on the ground, which is 30 m away from the foot of the tower, is 30°. Find the height of the tower

.

Q 6. A 1.5 m tall boy is standing at some distance from a 30 m tall building. The angle of elevation from his eyes to the top of the building increases from 30° to 60° as he walks towards the building. Find the distance he walked towards the building.

 

Q7. The angle of elevation of the top of a building from the foot of the tower is 30° and the angle of elevation of the top of the tower from the foot of the building is 60°. If the tower is 50 m high, find the height of the building.

 

Q8. From the top of a 7 m high building, the angle of elevation of the top of a cable tower is 60° and the angle of depression of its foot is 45°. Determine the height of the tower.

Q9. A straight highway leads to the foot of a tower. A man standing at the top of the tower observes a car at an angle of depression of 30°, which is approaching the foot of the tower with a uniform speed. Six seconds later, the angle of depression of the car is found to be 60°. Find the time taken by the car to reach the foot of the tower from this point.

Q10 .The angles of elevation of the top of a tower from two points at a distance of 4 m and 9 m from the base of the tower and in the same straight line with it are complementary. Prove that the height of the tower is 6 m.

 

 

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 

                                 thank you 

                     


       

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