5_6_inverse_trig_functions

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Unformatted text preview: 5_6_inverse_trig_functions_rev.notebook February 17, 2009 5.6 Inverse Trig Functions and Differentiation Extra HW: Use right triangle trig to derive d(arc cos u) dx Jump to Differentiation Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework Part 1 intro Prof. Battaly, WCC, Calc 2 1 5_6_inverse_trig_functions_rev.notebook February 17, 2009 5.6 Inverse Trig Functions and Differentiation Consider: Can find the inverse first, then substitute: Now, when x= 3, y = 0 is more obvious. Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework Part 1 intro Prof. Battaly, WCC, Calc 2 2 5_6_inverse_trig_functions_rev.notebook February 17, 2009 5.6 Inverse Trig Functions and Differentiation infinitely many x values for the domain of y = sin x Does not pass the horizontal line test for the whole domain of y = sinx Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework Part 1 y = sin x Prof. Battaly, WCC, Calc 2 3 5_6_inverse_trig_functions_rev.notebook February 17, 2009 5.6 Inverse Trig Functions and Differentiation Since y = sin x is not 1to1, we need to limit the domain to a portion where it is 1to1 Limit domain: -/2 X /2 Now, find the inverse function: Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework Part 1 inverse for y=sinx Prof. Battaly, WCC, Calc 2 4 5_6_inverse_trig_functions_rev.notebook February 17, 2009 5.6 Inverse Trig Functions and Differentiation Basic Trig Functions: Where are they 1to1? y = sin x /2 x /2 y = cos x 0 < x < y = tan x /2 < x < /2 Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework Part 1 where 1to1? Prof. Battaly, WCC, Calc 2 5 5_6_inverse_trig_functions_rev.notebook February 17, 2009 5.6 Inverse Trig Functions: sinx and arcsinx Remember reflective property of inverses. Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Inverse Sine Homework Part 1 Prof. Battaly, WCC, Calc 2 6 5_6_inverse_trig_functions_rev.notebook February 17, 2009 5.6 Inverse Trig Functions: cosx and arccosx Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Inverse Cosine Homework Part 1 Prof. Battaly, WCC, Calc 2 7 5_6_inverse_trig_functions_rev.notebook February 17, 2009 5.6 Inverse Trig Functions: tanx and arctanx Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework Part 1 Inverse Tangent Prof. Battaly, WCC, Calc 2 8 5_6_inverse_trig_functions_rev.notebook February 17, 2009 5.6 Inverse Trig Functions: Domain and Range Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework Part 1 inver Prof. Battaly, WCC, Calc 2 9 5_6_inverse_trig_functions_rev.notebook February 17, 2009 5.6 Inverse Trig Functions and Differentiation Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework Part 1 examples Prof. Battaly, WCC, Calc 2 10 5_6_inverse_trig_functions_rev.notebook February 17, 2009 5.6 Inverse Trig Functions and Differentiation (/4) Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework Part 1 examples Prof. Battaly, WCC, Calc 2 11 5_6_inverse_trig_functions_rev.notebook February 17, 2009 Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework Part 1 Feb 116:34 PM Prof. Battaly, WCC, Calc 2 12 5_6_inverse_trig_functions_rev.notebook February 17, 2009 Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework Part 1 Feb 116:37 PM Prof. Battaly, WCC, Calc 2 13 5_6_inverse_trig_functions_rev.notebook February 17, 2009 Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework Part 1 Feb 116:41 PM Prof. Battaly, WCC, Calc 2 14 5_6_inverse_trig_functions_rev.notebook February 17, 2009 5.6 Inverse Trig Functions and Differentiation Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework Part 1 examples Prof. Battaly, WCC, Calc 2 15 5_6_inverse_trig_functions_rev.notebook February 17, 2009 5.6 Inverse Trig Functions and Differentiation Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework Part 1 examples Prof. Battaly, WCC, Calc 2 16 5_6_inverse_trig_functions_rev.notebook February 17, 2009 5.6 Inverse Trig Functions and Differentiation Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework Part 1 examples Prof. Battaly, WCC, Calc 2 17 5_6_inverse_trig_functions_rev.notebook February 17, 2009 5.6 Inverse Trig Functions: Derivative of arcsinu d(arc sin u) = ? dx F: d/dx sin = u = arc sin u sin = u = opp = u hyp 1 1 u Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework Part 1 Derivative of arcsinu Prof. Battaly, WCC, Calc 2 18 5_6_inverse_trig_functions_rev.notebook February 17, 2009 5.6 Inverse Trig Functions and Differentiation Extra HW: Use right triangle trig to derive d(arc cos u) dx Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework Part 1 extra HW problem Prof. Battaly, WCC, Calc 2 19 5_6_inverse_trig_functions_rev.notebook February 17, 2009 5.6 Inverse Trig Functions and Differentiation inverse trig derivatives Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework Part 1 Deriv Inv Trig Funct Functions Prof. Battaly, WCC, Calc 2 20 5_6_inverse_trig_functions_rev.notebook February 17, 2009 5.6 Inverse Trig Functions and Differentiation inverse trig derivatives using trig: Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework Part 1 examples Prof. Battaly, WCC, Calc 2 21 5_6_inverse_trig_functions_rev.notebook February 17, 2009 5.6 Inverse Trig Functions and Differentiation inverse trig derivatives using formula: Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework Part 1 examples Prof. Battaly, WCC, Calc 2 22 5_6_inverse_trig_functions_rev.notebook 5.6 Inverse Trig Functions and Differentiation inverse trig derivatives February 17, 2009 using formula: using trig: Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework Part 1 algebra examples Prof. Battaly, WCC, Calc 2 23 5_6_inverse_trig_functions_rev.notebook February 17, 2009 Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework Part 1 Feb 117:19 PM Prof. Battaly, WCC, Calc 2 24 5_6_inverse_trig_functions_rev.notebook February 17, 2009 Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework Part 1 Feb 117:23 PM Prof. Battaly, WCC, Calc 2 25 5_6_inverse_trig_functions_rev.notebook February 17, 2009 using formula: Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework Part 1 Feb 117:27 PM Prof. Battaly, WCC, Calc 2 26 5_6_inverse_trig_functions_rev.notebook February 17, 2009 Feb 117:32 PM Prof. Battaly, WCC, Calc 2 27 5_6_inverse_trig_functions_rev.notebook February 17, 2009 inverse trig derivatives 5.6 Inverse Trig Functions and Differentiation Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework Part 1 examples Prof. Battaly, WCC, Calc 2 28 Attachments 5_6_inverse_trig_derivatives.png 5_6_inverse_trig_derivatives.jpg ...
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