(a). If x = 0 and y > 0 (y < 0), then Arg z = T/2 (-7/2). (b). If æ > 0, then Arg z = tan-(y/x) E (-T/2, 7/2). (c). If x <0 and y > 0 (y < 0), then Arg z = T). (d). Arg (212) uniquely chosen so that the LHS E (-T, 7]. In particular, let z1 = -1, 22 = -1, so that Arg z1 relation holds with m = -1. tan-(y/x)+T (tan-'(y/x)– Arg z1 + Arg 22 + 2mn for some integer m. This m is Arg z2 = T and Arg (21 22) = Arg(1) = 0. Thus the (e). Arg(21/2) = Arg z1 - Arg z2 + 2mm for some integer m. This m is uniquely chosen so that the LHS E (-T, 7].
(a). If x = 0 and y > 0 (y < 0), then Arg z = T/2 (-7/2). (b). If æ > 0, then Arg z = tan-(y/x) E (-T/2, 7/2). (c). If x <0 and y > 0 (y < 0), then Arg z = T). (d). Arg (212) uniquely chosen so that the LHS E (-T, 7]. In particular, let z1 = -1, 22 = -1, so that Arg z1 relation holds with m = -1. tan-(y/x)+T (tan-'(y/x)– Arg z1 + Arg 22 + 2mn for some integer m. This m is Arg z2 = T and Arg (21 22) = Arg(1) = 0. Thus the (e). Arg(21/2) = Arg z1 - Arg z2 + 2mm for some integer m. This m is uniquely chosen so that the LHS E (-T, 7].
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 91E
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![3.22. Observe that:
(a). If x = 0 and y > 0 (y < 0), then Arg z = 7/2 (-T/2).
(b). If r > 0, then Arg z = tan- (y/x) E (-T/2, 7/2).
(c). If x < 0 and y >0 (y < 0), then Arg z =
T).
(d). Arg (z122) = Arg z1 + Arg z2 + 2mm for some integer m. This m is
uniquely chosen so that the LHS E (-7, 7]. In particular, let z1 = -1, z2 =
-1, so that Arg z1 =
relation holds with m = -1.
tan-(y/x)+T (tan-(y/x) –
Arg z2 = T and Arg (212)
Arg(1)
= 0. Thus the
(e). Arg(21/2)
uniquely chosen so that the LHS E (-7, 7].
Arg z1 – Arg z2 + 2mn for some integer m. This m is](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff16e922a-c467-4ffd-adaf-e42dac6f3911%2F89e4ed94-c969-4daf-a2d1-30d47241b5fd%2Fxf7dls_processed.jpeg&w=3840&q=75)
Transcribed Image Text:3.22. Observe that:
(a). If x = 0 and y > 0 (y < 0), then Arg z = 7/2 (-T/2).
(b). If r > 0, then Arg z = tan- (y/x) E (-T/2, 7/2).
(c). If x < 0 and y >0 (y < 0), then Arg z =
T).
(d). Arg (z122) = Arg z1 + Arg z2 + 2mm for some integer m. This m is
uniquely chosen so that the LHS E (-7, 7]. In particular, let z1 = -1, z2 =
-1, so that Arg z1 =
relation holds with m = -1.
tan-(y/x)+T (tan-(y/x) –
Arg z2 = T and Arg (212)
Arg(1)
= 0. Thus the
(e). Arg(21/2)
uniquely chosen so that the LHS E (-7, 7].
Arg z1 – Arg z2 + 2mn for some integer m. This m is
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