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5.6 & 5.7 - Inverse Trig Functions - Differentiation & Integration

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pranitsingh524's version from 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 domainabsolute value of X is greater than or equal to 1
arccscx domainabsolute 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
memorize
List the six domains without looking.

 

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
memorize
List the six ranges w/out looking.

 

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
memorize

 

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
memorize