Home
Class 12
MATHS
Assume that theta is a rational multiple...

Assume that `theta` is a rational multiple of `pi` such that `cos theta` is a distinct rational. The number of values of `cos theta` is

A

3

B

4

C

5

D

6

Text Solution

Verified by Experts

The correct Answer is:
C
`theta=k pi, k=p/q, p, q in I, q ne 0`
`cos kpi` is a rational. Hence,
`k=0, 1, 1//2, 1//3, 2//3`
There are five values of `cos theta` for which `cos theta` is rational.
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC EQUATIONS

    CENGAGE|Exercise Exercise (Multiple)|31 Videos

  • TRIGONOMETRIC EQUATIONS

    CENGAGE|Exercise Exercise (Comprehension)|20 Videos

  • TRIGONOMETRIC EQUATIONS

    CENGAGE|Exercise Exercise 4.9|6 Videos

  • TRIGNOMETRIC RATIOS IDENTITIES AND TRIGNOMETRIC EQUATIONS

    CENGAGE|Exercise Question Bank|34 Videos

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE|Exercise SINGLE CORRECT ANSWER TYPE|38 Videos

Similar Questions

Explore conceptually related problems

If (tan theta)/(2)=cos ec theta-sin theta, then the numberical value of cos^(2)((theta)/(2)) is

If sin^2 theta = 1+cos^6 theta then number of values of theta in range (0, 2pi) is

If sin(pi cos theta)=cos(pi sin theta), then of the value cos(theta+-(pi)/(4)) is

If the system of linear equations {:((cos theta)x + (sin theta) y + cos theta=0),((sin theta)x+(cos theta)y + sin theta=0),((cos theta)x + (sin theta)y -cos theta=0):} is consistent , then the number of possible values of theta, theta in [0,2pi] is :

If |(cos theta,-1,1),(cos2 theta,4,3),(2,7,7)|=0 , then the number of values of theta in [0, 1pi] is

If |[cos theta,-1,1],[cos2 theta,4,3],[2,7,7]|=0 then the number of values of theta in [0,2 pi]

If sec theta=2cos theta , where (pi/2) lt theta lt pi , then what is the value of theta ?

If 2cos ec theta-cos theta cot theta>=k AA theta in(0,pi) then value of k is

When theta=11/3pi , then the value of cos theta-sin theta is

CENGAGE-TRIGONOMETRIC EQUATIONS-Exercise (Single)
  1. Number of solutions of the equation 4(cos^(2) 2x+ cos 2 x +1)+tan x (t...

    Text Solution

    |

  2. Let 0<theta1<theta2<theta3< denote the positive solution of the equati...

    Text Solution

    |

  3. Assume that theta is a rational multiple of pi such that cos theta is ...

    Text Solution

    |

  4. If x, y in [0, 2pi] and sin x + sin y=2, then the value of x+y is

    Text Solution

    |

  5. Number of roots of cos^2x+(sqrt(3)+1)/2sinx-(sqrt(3))/4-1=0 which lie ...

    Text Solution

    |

  6. The sum of all the solutions of cottheta=sin2theta(theta!=npi, n in t ...

    Text Solution

    |

  7. The number of solutions of 12 cos^(3) x-7 cos^(2) x+4 cos x=9 is

    Text Solution

    |

  8. Number of solutions of the equation sin x + cos x-2sqrt(2) sin x cos x...

    Text Solution

    |

  9. The general solution of (tan 5x-tan 4x)/(1+ tan 5 x tan 4x)=1 is

    Text Solution

    |

  10. If xsina+ysin2a+zsin3a=sin4a xsinb+ysin2b+zsin3b=sin4b xsinc+ysin2c+...

    Text Solution

    |

  11. The number of solutions of the equation sin 2 theta-2 cos theta +4 sin...

    Text Solution

    |

  12. The number of distinct real roots of the equation tan(2pix)/(x^2+x+1)=...

    Text Solution

    |

  13. The smallest positive value of x (in radians) satisfying the equation ...

    Text Solution

    |

  14. The number of solution of sin^(4)x-cos^(2) x sin x+2 sin^(2)x+sin x=0 ...

    Text Solution

    |

  15. The range of 'y, such that the equation in x, y + cos x = sin x has a ...

    Text Solution

    |

  16. Solution of the equation sin (sqrt(1+sin 2 theta))= sin theta + cos th...

    Text Solution

    |

  17. One of the general solutions of sqrt(3) cos theta -3 sin theta =4 sin ...

    Text Solution

    |

  18. The general solution of the equation 8 cos x cos 2x cos 4x = sin 6x//s...

    Text Solution

    |

  19. (sin^(3) theta-cos^(3) theta)/(sin theta - cos theta)- (cos theta)/sqr...

    Text Solution

    |

  20. For 0<x , y<pi, the number of ordered pairs (x , y) satisfying the sys...

    Text Solution

    |