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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.
 Spring '11
 foad
 Calculus

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