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 ENGLISH|Exercise Exercises (Multiple correct type)|31 Videos

  • TRIGONOMETRIC EQUATIONS

    CENGAGE ENGLISH|Exercise Exercises (Linked comprehension type)|20 Videos

  • TRIGONOMETRIC EQUATIONS

    CENGAGE ENGLISH|Exercise Concept Application Exercise 4.9|6 Videos

  • THREE-DIMENSIONAL GEOMETRY

    CENGAGE ENGLISH|Exercise ARCHIVES INTEGER TYPE|1 Videos

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE ENGLISH|Exercise SINGLE CORRECT ANSWER TYPE|38 Videos

Similar Questions

Explore conceptually related problems

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

If sin theta =sqrt(3) cos theta, -pi lt theta lt 0 , then the value of theta is

if a cos theta + b sin theta = c. then what is the value of a sin theta -b cos theta

If sin theta+ cos theta = sqrt(2) cos theta, (theta ne 90^(@)) then value of tan theta is

If a cos theta-b sin theta = c, then find the value of a sin theta + b cos theta.

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 costheta+cos3theta+cos5theta+cos7theta=0 , then general value of theta is:

If cos(theta-phi) , cos(theta) , cos(theta+phi) are in HP, the the value of cos(theta)sec(phi/2) is

If pi < theta < 2pi and z=1+cos theta + i sin theta , then write the value of |z|

CENGAGE ENGLISH-TRIGONOMETRIC EQUATIONS-Exercises (Single Correct Answer Type)
  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

    |