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Math 112 Quiz 5: Trigonometric Identities and Values, Quizzes of Mathematics

University of Oregon (UO)Mathematics

A math quiz consisting of true or false questions and computational problems based on trigonometric identities and values. Students are required to justify their answers for the true or false questions and find the exact values for the computational problems.

Typology: Quizzes

Pre 2010

Uploaded on 07/29/2009

koofers-user-6n2
koofers-user-6n2 🇺🇸

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Name: 2/21/07
Math 112 Quiz 5
1. (3pts each) True or False ? (justify your answers)
(a) arccos(cos(x)) = xfor all real numbers x.
(b) arctan(31) is undefined.
2. (2pts each) Find the exact value of each of the following.
(a) arcsin(−1)
(b) cos(arcsin(−
1
2))
(c) tan(arctan(2))
(d) arcsin(sin(7π))
(e) arccos(sin(0)) −sin(arccos(0))
pf2

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Name: (^) Math 112 Quiz 5 2/21/

  1. (3pts each) True or False? (justify your answers)(a) arccos(cos(x)) = x for all real numbers x.

(b) arctan(31) is undefined.

  1. (2pts each) Find the exact value of each of the following.(a) arcsin(−1) (b) cos(arcsin(−^12 )) (c) tan(arctan(2)) (d) arcsin(sin(7π)) (e) arccos(sin(0)) − sin(arccos(0))
  1. (5pts) Find the exact value of tan ( 2 arccos ( − 2 3 ))^. Hint: the double-angle identity for tangent is tan(2x) = 1 2 tan(−tan 2 x()x)