Home
Class 12
MATHS
If sintheta=1/2a n dcostheta=-(sqrt(3))/...

If `sintheta=1/2a n dcostheta=-(sqrt(3))/2,` then the general value of `theta` is `(n in Z)`

A

`2n pi+(5pi)/6`

B

`2n pi+pi/6`

C

`2n pi+(7pi)/6`

D

`2npi+pi/4`

Text Solution

Verified by Experts

The correct Answer is:
A
`sin theta=1//2` and `cos theta=-sqrt(3)//2`
`rArr theta` lies in the second quadrant.
`rArr sin theta=sin 5pi//6`,
`:. Theta=2npi+(5pi//6), n in Z`
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 sin theta=(1)/(2) and cos theta=-(sqrt(3))/(2), then the general value of theta is (n in Z)*( a) 2n pi+(5 pi)/(6) (b) 2n pi+(pi)/(6)2n pi+(7 pi)/(6)( d) 2n pi+(pi)/(4)

If sin theta = 1//2 and cos theta = -sqrt(3)//2 , then the general value of theta is

If sin theta=(1)/(2) and cos theta=(sqrt(3))/(2) then the general value of theta which satisfies both the equations is

If cos 2theta=(sqrt(2)+1)(cos theta-(1)/(sqrt(2))) , then the general value of theta(n in Z)

If tantheta=-(1)/(sqrt(3)),sintheta=(1)/(2)andcostheta=-(sqrt(3))/(2) , then the principal value of theta will be

If 4sin^(2)theta+2(sqrt(3)+1)cos theta=4+sqrt(3) then the general value of theta is

If tan^(2)theta-(1+sqrt(3))tan theta+sqrt(3)=0, then the general value of theta is

If tan^(2)theta-(1+sqrt(3))tan theta+sqrt(3)=0, then the general value of theta is

If sintheta=-1/2 and tantheta=1/sqrt(3) then theta is equal to,

CENGAGE-TRIGONOMETRIC EQUATIONS-Exercise (Single)
  1. If sintheta=1/2a n dcostheta=-(sqrt(3))/2, then the general value of t...

    Text Solution

    |

  2. The most general value for which tantheta = -1 " and " costheta = 1/(s...

    Text Solution

    |

  3. Sum of roots of the equation x^2-2x^2sin^2(pix)/2+1=0 is

    Text Solution

    |

  4. The number of solutions of the pair of equations 2s in^2theta-cos2thet...

    Text Solution

    |

  5. Number of solutions of equation 2"sin" x/2 cos^(2) x-2 "sin" x/2 sin^(...

    Text Solution

    |

  6. Number of solutions of the equation 4(cos^(2) 2x+ cos 2 x +1)+tan x (t...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |