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. If A is an acute angle and sin A = 3/5, find all other trigonometric ratios of angle A (using trigonometric identities).

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Book- ML Aggarwal
Board- ICSE
Publication- Avichal
Chapter- Trigonometric Identities
Chapter number-18

 If A is an acute angle and sin A = 3/5, find all other trigonometric ratios of angle A (using trigonometric identities).

Q no. 1, M L Aggarwal, trigonometric identities

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1 Answer

  1. We have been given that

    sin A = 3/5 and A is an acute angle

     

    So, in ∆ABC we have ∠B = 90o

     

    And,

     

    AC = 5 and BC = 3

     

    By Pythagoras theorem,

     

    AB = √(AC2 – BC2)

     

    = √(52 – 32) = √(25 – 9) = √16

     

    = 4

     

    Now,

     

    cos A = AB/AC = 4/5

     

    tan A = BC/AB = 3/4

     

    cot A = 1/tan θ = 4/3

     

    sec A = 1/cos θ = 5/4

     

    cosec A = 1/sin θ = 5/3

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