Home
Class 12
MATHS
Evaluate each of the following: sin...

Evaluate each of the following:

`sin^(-1)(sin3)`

(ii) `sin^(-1)(sin4)`

Text Solution

AI Generated Solution

To evaluate the expressions \( \sin^{-1}(\sin 3) \) and \( \sin^{-1}(\sin 4) \), we need to understand the properties of the inverse sine function and the sine function. ### Step-by-Step Solution: 1. **Understanding the Range of \( \sin^{-1}(x) \)**: The function \( \sin^{-1}(x) \) (or arcsin) has a range of \( \left[-\frac{\pi}{2}, \frac{\pi}{2}\right] \). This means that for any angle \( x \) outside this range, we need to find a corresponding angle within this range that has the same sine value. 2. **Evaluating \( \sin^{-1}(\sin 3) \)**: ...
Promotional Banner

Topper's Solved these Questions

  • INDEFINITE INTEGRALS

    RD SHARMA|Exercise Solved Examples And Exercises|1401 Videos
  • JEE MAINS PREVIOUS YEAR

    RD SHARMA|Exercise EXAMPLE|1 Videos

Similar Questions

Explore conceptually related problems

Evaluate each of the following: sin^(-1)(sin12) (ii) sin^(-1)(sin2)

Evaluate each of the following: sin^(-1)((sin pi)/(6)) (ii) sin^(-1)((sin(7 pi))/(6))( iii) sin^(-1)((sin(5 pi))/(6))

Evaluate each of the following: sin^(-1)((sin(13 pi))/(7))( ii) sin^(-1)((sin(17 pi))/(8))( iii) sin^(-1){(s in-(17 pi)/(8))}

Evaluate the following: sin^(-1)(sin10)( ii) sin^(-1)(sin5)

Evaluate each of the following: sin^(-1)((sin pi)/(3)) (ii) cos^(-1)((cos(2 pi))/(3))( iii) tan^(-1)((tan pi)/(4))

Evaluate each of the following: sin^(-1)(sin(pi)/(3)) (ii) cos^(-1)(cos(2 pi)/(3))tan^(-1)(tan(pi)/(4))(iv)sin^(-1)(sin(2 pi)/(3))cos^(-1)(cos(7 pi)/(7))(vi)tan^(-1)(tan(3 pi)/(4))sin^(-1)(cos(-600^(@))cos^(-1)(cos(-680^(@)))

Evaluate each of the following: sin((sin^(-1)5)/(13)) (ii) sin((cos^(-1)4)/(5))( iii) sin((tan^(-1)(15))/(8))

Evaluate each of the following: sin^(-1)((sin(2 pi))/(3))( ii) cos^(-1)((cos(7 pi))/(6))( iii) tan^(-1)((tan(3 pi))/(4))

Evaluate each of the following: sin((cot^(-1)4)/(3)) (ii) sin((sec^(-1)(17))/(15)) (iii) sin(csc^(-1)(17)/(8))

Evaluate each of the following: sin^(-1)(sin(-600o))(ii)cos^(-1)(cos(-6800))

RD SHARMA-INVERSE TRIGONOMETRIC FUNCTION-Solved Examples And Exercises
  1. Evaluate each of the following: (i)sin^(-1)(sinpi/6) (ii) sin^...

    Text Solution

    |

  2. Evaluate each of the following: (i)sin^(-1)(sin((13pi)/7)) (ii...

    Text Solution

    |

  3. Evaluate each of the following: sin^(-1)(sin3) (ii) sin^(-1)(s...

    Text Solution

    |

  4. Evaluate each of the following: (i)sin^(-1)(sin12) (ii) sin^(-...

    Text Solution

    |

  5. Evaluate each of the following: (i)cos^(-1){cos(-pi/4)} (ii) c...

    Text Solution

    |

  6. Evaluate each of the following: (i)cos^(-1)(cos((13pi)/6)) (ii...

    Text Solution

    |

  7. Evaluate each of the following: (i)cos^(-1)(cos5) (ii) cos^(-1...

    Text Solution

    |

  8. Evaluate each of the following: (i)tan^(-1)(tanpi/3) (ii) tan^...

    Text Solution

    |

  9. Evaluate each of the following: (i)tan^(-1)(tan((9pi)/4)) (ii)...

    Text Solution

    |

  10. Evaluate each of the following: (i)tan^(-1)(tan4) (ii) tan^(-1...

    Text Solution

    |

  11. Evaluate each of the following: (i)sec^(-1)(secpi/3) (ii) sec^(-...

    Text Solution

    |

  12. Evaluate each of the following: sec^(-1)(sec(7pi)/3) (ii) sec^(-1)(...

    Text Solution

    |

  13. Evaluate each of the following: sec^(-1)(sec(13pi)/4) (ii) sec^(-1)...

    Text Solution

    |

  14. Evaluate each of the following: "c o s e c"^(-1)("c o s e c"pi/4) (...

    Text Solution

    |

  15. Evaluate each of the following: (i) "c o s e c"^(-1)("c o s e c"(...

    Text Solution

    |

  16. Evaluate each of the following: (i) "c o s e c"^(-1)("c o s e c"(...

    Text Solution

    |

  17. Evaluate each of the following: (i)cot^(-1)(cotpi/3) (ii) cot^(...

    Text Solution

    |

  18. Evaluate each of the following: (i)cot^(-1)(cot(19pi)/6) (ii)...

    Text Solution

    |

  19. Write each of the following in the simplest form: cot^(-1){a/(sqrt(x...

    Text Solution

    |

  20. Write each of the following in the simplest form: (i)tan^(-1){sqr...

    Text Solution

    |