Math 112 Spring 2004 Midterm 2 Practice Exam, Exams of Mathematics

A practice midterm exam for math 112, spring 2004. The exam covers various topics related to trigonometric functions, including true or false questions, graph drawing, evaluating expressions, finding values of trigonometric functions, and proving identities. Students are required to show their work for some problems.

Typology: Exams

Pre 2010

Uploaded on 07/23/2009

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Practice MIDTERM 2 Math 112 Spring2004
NAME:
1. [5] TRUE/FALSE: Circle T in each of the following cases if the statement is always
true. Otherwise, circle F. Let θbe a real number and kand integer.
T F cot θis the slope of the terminal side of θ
T F The domain of tan1θis [1,1]
T F cot(θ) = cot θ
T F The sec function is an even function.
T F The range of cos1is [0, π]
T F The range of cos θis [0, π]
T F csc 2θ=1
2 sin θcos θ
T F cos(θ+ 3θ) = cos θ+ cos 3θ
T F cos(θ+ 3θ) = cos θcos 3θsin θsin 3θ
T F ln e0= 0
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Practice MIDTERM 2 Math 112 Spring

NAME:

  1. [5] TRUE/FALSE: Circle T in each of the following cases if the statement is always true. Otherwise, circle F. Let θ be a real number and k and integer.

T F cot θ is the slope of the terminal side of θ

T F The domain of tan−^1 θ is [− 1 , 1]

T F cot(−θ) = − cot θ

T F The sec function is an even function.

T F The range of cos−^1 is [0, π]

T F The range of cos θ is [0, π]

T F csc 2θ =

2 sin θ cos θ

T F cos(θ + 3θ) = cos θ + cos 3θ

T F cos(θ + 3θ) = cos θ cos 3θ − sin θ sin 3θ

T F ln e^0 = 0

Show your work for the following problems. The correct answer with no

supporting work will receive NO credit.

  1. [3] Give the complete graphs for cos θ, csc θ, and cos θ. No points are given if your graph has no labels or units.
  2. [5] Evaluate: csc − 65 π csc2 7 6 π − cot2 7 6 π

sec(− 34 π ) csc π 6 cot 6076 π

  1. [4] Simplify: 3(

2)−^1 cos^2 x (sin^3 x)(

6)(cot x)(csc x)

  1. [3] Prove for all x in the domain:

sin x − sin 3x cos x − cos 3x

= − cot 2x

hint: think factor identites

  1. [4] Prove for all x in the domain: cos^2 x(sec x + 1)^2 = (1 + cos x)^2
  1. [7] Induction: Prove that for all positive integers n:

∑^ n

i=

2 i^

2 n