Home
Class 12
MATHS
The total number of solution of sin {x}=...

The total number of solution of `sin {x}= cos {x}` (where {.} denotes the fractional part) in `[0, 2pi]` is equal to

Text Solution

Verified by Experts

Given the equation is `sin {x} = cos {x}.`
`tan {x} = 1`
`tan (pi//4) = 1 lt tan 1`

The graphs of `y = tan {x}` and y = 1 meet exactly six times in `[0, 2pi]`.
Promotional Banner

Topper's Solved these Questions

  • GRAPHS OF TRIGONOMETRIC FUNCTIONS

    CENGAGE|Exercise Exercise|22 Videos

  • GRAPHS OF ELEMENTARY FUNCTIONS

    CENGAGE|Exercise Exercise|34 Videos

  • HIGHT AND DISTANCE

    CENGAGE|Exercise JEE Previous Year|3 Videos

Similar Questions

Explore conceptually related problems

If total number of solution of sin{y}=cos{y} where {y} denotes the fractional part of y and y in[0,3 pi] is c then total number of integral values of b for which the equation x^(2)+bx+c=0 have imaginary roots.

The number of solutions of [sin x]=cos x where [.] denotes the greatest integer function in [0,3 pi], is equal to

Evaluate int_(0)^(2){x} d x , where {x} denotes the fractional part of x.

The value of int_(0)^(4) {x} dx (where , {.} denotes fractional part of x) is equal to

The number of solutions of 4{x}=x+ [x] where [.] denotes G.I.F and {.} represents fractional part function is equal to

Total number of solutions of [sin x]+cos x=0, where [] denotes the greatest integer function,for x e [0,100 pi] is (A) 100 (B) 50 (C) 25 (D) 0

The period of function 2^({x}) +sin pi x+3^({x//2})+cos pi x (where {x} denotes the fractional part of x) is

Period of the function f(x)=cos(cos pi x)+e^({4x}), where {.} denotes the fractional part of x, is

lim_(x rarr1)(x sin{x})/(x-1)," where "{x}" denotes the fractional part of "x," is equal to "

CENGAGE-GRAPHS OF TRIGONOMETRIC FUNCTIONS-Exercise
  1. Draw the graph of y = cos^(2)x.

    Text Solution

    |

  2. Find the values of x for which f(x) = sqrt(sin x - cos x) is defined.

    Text Solution

    |

  3. Draw the graph of y = tan^(2) x.

    Text Solution

    |

  4. Draw the graph of y = sin x + cos x, x in [0, 2pi].

    Text Solution

    |

  5. Draw the graph of y = [cos x], x in [0, 2pi], where [*] represents the...

    Text Solution

    |

  6. Draw the graph of y = sin pisqrt(x).

    Text Solution

    |

  7. Find the number of roots of the equation x sin x = 1, x in [-2pi, 0) ...

    Text Solution

    |

  8. Evaluate : [lim(x to 0) (tan x)/(x)], where [*] represents the greates...

    Text Solution

    |

  9. For f(x) = sin x - x^(2) + 1, check weather the function is increasing...

    Text Solution

    |

  10. Draw the graph of the function f(x)=m a xdot{sinx ,cos2x},x in [0,2pi]...

    Text Solution

    |

  11. Draw the graph of [y] = cos x, x in [0, 2pi], where [*] denotes the g...

    Text Solution

    |

  12. The total number of solution of sin {x}= cos {x} (where {.} denotes th...

    Text Solution

    |

  13. Draw the graph of f(x) = |tan x| + |cot x|.

    Text Solution

    |

  14. Find the number of solutions to cos x = (x)/(10), x gt 0.

    Text Solution

    |

  15. The number of solutions of tanx-m x=0,m >1, in (-pi/2,pi/2) is 1 (b) 2...

    Text Solution

    |

  16. Find the number of solutions to log(e) |sin x| = -x^(2) + 2x in [-(pi)...

    Text Solution

    |

  17. Solve :cos x le - (1)/(2).

    Text Solution

    |

  18. Prove that the least positive value of x , satisfying tanx=x+1, lies i...

    Text Solution

    |

  19. Draw the graph of y = (x^(2))/(10) sin x.

    Text Solution

    |

  20. Draw the graph of y = (sin x)/(x).

    Text Solution

    |