Home
Class 12
MATHS
Find the range of f(x)=sqrt(sin^2x-8sinx...

Find the range of `f(x)=sqrt(sin^2x-8sinx+16)+2`.

Text Solution

Verified by Experts

`f(x)=sqrt(sin^2X-6sinx+9)+3`
`=sqrt((sinx-3)^2)+3`
`=abs(sinx-3)+3`
Now, `-1lesinxle1`
or `-4lesinx-3le-2`
or `2leabs(sinx-3)le4`
or `5leabs(sinx-3)+3le7`
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE PUBLICATION|Exercise example|10 Videos

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE PUBLICATION|Exercise Concept Application Exercises 2.1|8 Videos

  • TRIGONOMETRIC EQUATIONS

    CENGAGE PUBLICATION|Exercise Archives (Numerical value type)|4 Videos

  • TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS

    CENGAGE PUBLICATION|Exercise Archives (Numerical Value Type)|2 Videos

Similar Questions

Explore conceptually related problems

Find the range of f(x)=sqrt(sin^2x-6sinx+9)+3

Find the range of f(x) =sin^2x-5sinx+6 .

Find the range of f(x)=sin^2x-3sinx+2

Find the range of f(x)=sin^2x-sinx+1.

Find the range of f(x) =8/(sinx+3)

Find the range of f(x)=1/(5sinx-6)

Find the range of f(x)=sin(cosx).

Find the range of f(x)=cos^4x+sin^2x-1 .

Find the range of f(x)=sgn(x^2-2x+3)

Find the range of f(x)=1/(1-3sqrt(1-sin^2x))

CENGAGE PUBLICATION-TRIGONOMETRIC FUNCTIONS -SINGLE CORRECT ANSWER TYPE
  1. Find the range of f(x)=sqrt(sin^2x-8sinx+16)+2.

    Text Solution

    |

  2. The circular wire of diameter 10 cm is cut and placed along the circum...

    Text Solution

    |

  3. Find the cartesian co-ordinates of the points whose polar co-ordinates...

    Text Solution

    |

  4. If theta in (pi//4, pi//2) and sum(n=1)^(oo)(1)/(tan^(n)theta)=sin the...

    Text Solution

    |

  5. Find the cartesian co-ordinates of the points whose polar co-ordinates...

    Text Solution

    |

  6. Find the cartesian co-ordinates of the points whose polar co-ordinates...

    Text Solution

    |

  7. Find the cartesian co-ordinates of the points whose polar co-ordinates...

    Text Solution

    |

  8. If (sin^(2)x-2cos^(2)x+1)/(sin^(2)x+2cos^(2)x-1)=4, then the value of ...

    Text Solution

    |

  9. Find the cartesian co-ordinates of the points whose polar co-ordinates...

    Text Solution

    |

  10. If tantheta-cottheta=aandsintheta+costheta=b, then, (b^2-1)^2(a^2+4...

    Text Solution

    |

  11. The least value of 18 sin^(2)theta+2 cosec^(2)theta-3 is (a) -15 (b) ...

    Text Solution

    |

  12. Find the cartesian co-ordinates of the points whose polar co-ordinates...

    Text Solution

    |

  13. Find the cartesian co-ordinates of the points whose polar co-ordinates...

    Text Solution

    |

  14. Find the cartesian co-ordinates of the points whose polar co-ordinates...

    Text Solution

    |

  15. Simplify :cos(x-(pi)/(2)).tan((3pi)/(2)+x)

    Text Solution

    |

  16. Consider angles alpha = (2n+(1)/(2))pi pm A and beta = m pi +(-1)^(m)(...

    Text Solution

    |

  17. Which of the following is true ?

    Text Solution

    |

  18. If the angle A of a triangle ABC is given by the equation 5 cos A + 3 ...

    Text Solution

    |

  19. Which of the following is greatest ?

    Text Solution

    |

  20. The number of value/values of x for which sin y=x^(2)-2x si possible i...

    Text Solution

    |

  21. Which of the following is not correct ?

    Text Solution

    |