Trigonometric Functions

  • Question 1
    CBSEENMA11013620

    Find the values of x and y when.

    space space space space space space space space left parenthesis 2 straight x comma space straight x plus straight y right parenthesis space equals space left parenthesis 6 comma space 2 right parenthesis

    Solution

     

    (2x, x + y) = (6, 2)
    rightwards double arrow   2x = 6  or x = 3
    and       x + y = 2 or  3+y = 2 or y = -1
    Hence, x = 3, y = -1

    Question 2
    CBSEENMA11013621

    space space space space space space space space open parentheses straight x over 3 plus 1 comma space straight y minus 2 over 3 close parentheses equals open parentheses 5 over 3 comma 1 third close parentheses,  find the values of x and y.

    Solution
    space space space space space space space space space space space space space space space space open parentheses straight x over 3 plus 1 comma space straight y minus 2 over 3 close parentheses equals open parentheses 5 over 3 comma 1 third close parentheses
    rightwards double arrow      space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space straight x over 3 plus 1 equals 5 over 3 space space or space straight x over 3 equals 5 over 3 or space straight x space equals space 2

    and           space space space space space space space space space space space space space space space space space space space space space space space space space space space straight y minus 2 over 3 equals 1 third or space straight y equals 1 third plus 2 over 3 equals 3 over 3 or space straight y equals 1
    Hence, x =2, y =1
    Question 3
    CBSEENMA11013626

    Find the values of x and y when

    (x2--x, y-3y+2)=(0, 0)

    Solution

    (x-x, y-3y+2) = (0, 0)
    rightwards double arrow        x-x = 0 or x(x-1)=0 or x = 0, 1
    and y-3y+2 = 0 or (y-1) (y-*2) = 0 or y = 1, 2
    Hence,  x = 0, x = 1, y = 1, y = 2

    Question 4
    CBSEENMA11013632

    If A = {a, b, c} and B = {p, q}, then find :

    (i) A x B (ii) B x A (iii) A x A (iv) B x B (v) n (A x B) (vi) n (B x A) (vii) n (A x A) (viil) n (B x B).

    Solution

    (i) A  X B = {a, b, c} x (p, q} = {{a, p}, {a, q}, (b, p}, {b, q}, {c, p}, {c, q}}
    (ii) B x A = {p, q} x {a, b, c} = {{p, a, }.{p, b}.{p, c}.{q, a}.{q, b}.{q, c}}
    (iii} A x A = {a, b, c} x {a, b, c} = {(a, a), (a, b), (a, c), (b,l, a), (b,, b), (b, c), (c a), (c, b), (c, c)}
    (iv) B x B = {p.q} x {p.q} = {(p.p), (p.q), (p.q), (p.q)
    (v) n(A x B) = n(A) x n(B) = 3 x 2 = 6
    (vi) n(B xA) = n(B) x n(A) = 2 x 3 = 6
    (vii) n(A xA) = n(A)  x n(A) = 3 x 3 = 9
    (viii) n(B x B) = n(B) x n(B) = 2 x 2 = 4

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