0000Inv Trig Fncs-Values

0000Inv Trig Fncs-Values - Values Involving Inverse...

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Unformatted text preview: Values Involving Inverse Trigonometric Functions II ( Finding arctrg(trgθ Examples I Arcsin arcsin[sin( - π/ 4 (] = - π/ 4 Notice that: - π/ 4 belongs to the range of the function y = arcsinx, which is [ -π/2 , π/2 ] Arctan arctan[tan( - π/ 4 (] = - π/ 4 Notice that: - π/ 4 belongs to the range of the function y = arctanx, which is ( -π/2 , π/2 ( Arccos arccos[cos( 3π/ 4 (] = 3π/ 4 Notice that: 3π/ 4 belongs to the range of the function y = arccosx, which is [ 0 , π ] Arccot arccot[cot( 3π/ 4 (] = 3π/ 4 Notice that: 3π/ 4 belongs to the range of the function y = arccotx, which is ( 0 , π ( Arcsec arcsec[sec( 5π/ 4 (] = 5π/ 4 Notice that: 5π/ 4 belongs to the range of the function y = arcsecx, which is [ 0 , π/2 ( U [π , 3π/2 ( Examples II Arcsin arcsin[sin( 3π/ 4 (] Notice that: 3π/ 4 does not belong to the range of the function y = arcsinx, which is [ -π/2 , π/2 ] sin( 3π/ 4 ( = 1/√2 ( Why? ( Thus, arcsin[sin( 3π/ 4 (] = arcsin[1/√2] = π/ 4 Arctan arctan[tan( 7π/ 4 (] Notice that: 7π/ 4 does not belong to the range of the function y = arctanx, which is ( -π/2 , π/2 ( tan( 7π/ 4 ( = -1 ( Why? ( Thus, arctan[tan( 7π/ 4 (] = arcsin[-1] = -π/ 4 Arccos arccos[cos( - π/ 4 (] Notice that: -π/ 4 does not belong to the range of the function y = arccosx, which is [ 0 , π ] cos( - π/ 4 ( = 1/√2 ( Why? ( Thus, arccos[cos( -π/ 4 (] = arccos[1/√2] = π/ 4 Arccot arccot[cot( 7π/ 4 (] Notice that: 7π/ 4 does not belong to the range of the function y = arccotx, which is ( 0 , π ( cot( 7π/ 4 ( = -1 ( Why? ( Thus, arccot[cot( 7π/ 4 (] = arccot[-1] = 3π/ 4 Arcsec arcsec[sec( 3π/ 4 (] Notice that: 3π/ 4 does not belong to the range of the function y = arcsecx, which is [ 0 , π/2 (U[π,3π/2( sec( 3π/ 4 ( = - √2 ( Why? ( Thus, arcsec[sec( 3π/ 4 (] = arcsec[ - √2] = 5π/ 4 ...
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This note was uploaded on 10/12/2011 for the course MATH 201 taught by Professor Foad during the Spring '11 term at Qatar University.

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0000Inv Trig Fncs-Values - Values Involving Inverse...

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