# 5.6 & 5.7 - Inverse Trig Functions - Differentiation & Integration

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2016-09-12 01:26

## Section

5.6

Question | Answer |
---|---|

arcsinx domain | [-1, 1] |

arccosx domain | [-1, 1] |

arctanx domain | (-infinity, infinity) |

arccotx domain | (-infinity, infinity) |

arcsecx domain | absolute value of X is greater than or equal to 1 |

arccscx domain | absolute value of X is greater than or equal to 1 |

which arc has the domain (-infinity, infinity) ? | tan & cot |

which arc have the domain [-1, 1] ? | sin & cos |

which arc have the domain absolute value of X is greater than or equal to 1 ? | sec & csc |

which arc has the range with the following brackets [ ] ? | sin, cos, sec, csc |

which arc has the range with the following brackets ( ) ? | tan, cot |

Question | Answer |
---|---|

arcsinx range | [-pie/2, pie/2] |

arccosx range | [0, pie] |

arctanx range | (-pie/2, pie/2) |

arccotx range | (0, pie) |

arcsecx range | [0, pie] but y cannot equal pie/2 |

arccscx range | [-pie/2, pie/2] but y cannot equal 0 |

when evaluating inverse trig functions, what unit are we using to denote the angles? | radians |

which arc has the range, [-pie/2, pie/2] ? | sin |

which arc has the range [-pie/2, pie/2] but y CAN'T equal 0? | csc |

which arc has the range [0, pie]? | cos |

which arc has the range (0, pie)? | cot |

which arc has the range [0, pie] but y CAN'T equal pie/2? | sec |

which arc has the range (-pie/2, pie/2)? | tan |

which arc has the range with the following brackets [ ] ? | sin, cos, sec, csc |

which arc has the range with the following brackets ( ) ? | tan, cot |

which arc has the following constraint, y cannot equal pie/2 ? | sec |

which arc has the following constraint, y cannot equal 0 ? | csc |

which arc have the constraints? | sec, csc |

Pg. 367

Draw arcsinx. Label domain and range.

Draw arccosx. Label domain and range.

draw arctanx. Label domain and range.

draw arccscx. Label domain and range.

draw arcsecx. label domain and range.

draw arccotx. label domain and range.

Find arcsin(-1/2)

find arccos0

find arctan of square root of 3

find arcsin(0.3)

Question | Answer |
---|---|

what is the derivative of arcsinu? | u' / √1 - u² |

what is the derivative of arccosu? | -u' / √1 - u² |

what is the derivative of arctanu? | u' / 1 + u² |

what is the derivative of arccotu? | -u' / 1 + u² |

what is the derivative of arcsecu? | u' / |u| √u² - 1 |

what is the derivative of arccscu? | -u' / |u| √u² - 1 |

which of the arc derivatives have an absolute value of u? | sec & csc |

which of the arc derivatives are negative ? (hint: all of them start with the same letter) | cos, cot, csc |

which of the arc derivatives have √1 - u² ? | sin & cos |

which of the arc derivatives have √u² - 1 ? | sec & csc |

which of the arc derivatives have 1 + u² ? | tan & cot |

5.7

Question | Answer |
---|---|

what is the integral of du / √a² - u² ? | arcsin u/a + C |

what is the arcsin u/a + C equation ? (hint: use integral!) | integral of du / √a² - u² ? |

what is the integral of du / √a² + u² ? | 1/a arctan u/a + C |

what is the 1/a arctan u/a + C equation? | integral of du / √a² + u² |

what is the integral of du / u √u² - a² ? | 1/a arcsec |u|/a + C |

what is the 1/a arcsec |u|/a + C equation ? | integral of du / u √u² - a² |

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